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Greg Biffle
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Greg Biffle
Biffle at the 2015 Toyota/Save Mart 350
Born
Gregory Jack Biffle
(1969-12-23) December 23, 1969 (age 48)
Vancouver, Washington
Height
5 ft 9 in (1.75 m)
Weight
170 lb (77 kg)
Achievements
2002 NASCAR Busch Series Champion
2000 NASCAR Craftsman Truck Series Champion
2005, 2006 Southern 500 Winner
2015, 2016 Sprint Showdown winner
Awards
2001 NASCAR Busch Series Rookie of the Year
1998 NASCAR Craftsman Truck Series Rookie of the Year
2002 NASCAR Busch Series Most Popular Driver
Monster Energy NASCAR Cup Series career
510 races run over 15 years
2016 position
23rd
Best finish
2nd (2005)
First race
2002 NAPA Auto Parts 500 (Fontana)
Last race
2016 Ford EcoBoost 400 (Homestead)
First win
2003 Pepsi 400 (Daytona)
Last win
2013 Quicken Loans 400 (Michigan)
Wins
Top tens
Poles
19 174 13
NASCAR Xfinity Series career
244 races run over 11 years
Best finish
1st (2002)
First race
1996 AC-Delco 200 (Rockingham)
Last race
2010 TECH-NET Auto Service 300 powered by Carquest (Charlotte)
First win
2001 Pepsi 300 (Nashville)
Last win
2009 Bashas' Supermarkets 200 (Phoenix)
Wins
Top tens
Poles
20 149 14
NASCAR Camping World Truck Series career
81 races run over 5 years
Best finish
1st (2000)
First race
1998 Chevy Trucks Challenge (Orlando)
Last race
2004 Ford 200 (Homestead)
First win
1999 Memphis 200 (Memphis)
Last win
2001 Chevy Silverado 150 (Phoenix)
Wins
Top tens
Poles
16 54 12
Statistics current as of November 20, 2016.
Gregory Jack Biffle (born December 23, 1969) is an American professional stock car racing driver. He last drove in 2016, last driving in the No. 16 Ford Fusion for Roush Fenway Racing. After racing in the NASCAR Winter Heat Series in the mid-1990s, he was recommended to Jack Roush by former announcer Benny Parsons. He was the 1998 NASCAR Craftsman Truck Series Rookie of the Year. He won the 2000 Craftsman Truck championship. He reprised this progression in the NASCAR Busch Series, winning the 2001 Rookie of the Year, immediately followed by winning the 2002 championship. Biffle drove in the NASCAR Sprint Cup Series for Roush from 2003 until 2016, winning 19 races in the No. 16 Ford. He currently is an analyst for NBC Sports' show NASCAR America.
Biffle, who began his NASCAR career in 1995, is the first of only three drivers that have won a championship in both the Busch Series and the Craftsman Truck Series, and the sixth of only twenty-nine drivers to win a race in each of NASCAR's three national series.
Contents
[hide]
1 Racing career
1.1 Craftsman Truck Series
1.2 Busch Series
1.3 Cup Series
2 Personal life
2.1 Appearances in media
2.2 Greg Biffle Foundation
3 Motorsports career results
3.1 NASCAR
3.1.1 Sprint Cup Series
3.1.1.1 Daytona 500
3.1.2 Nationwide Series
3.1.3 Craftsman Truck Series
3.2 International Race of Champions
3.3 24 Hours of Daytona
4 See also
5 References
6 External links
Racing career[edit]
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Biffle was born and raised in Camas, Washington.[1] He began his racing career driving on short tracks around the Pacific Northwest. He first gained attention as a driver when he raced in the nationally televised Winter Heat Series in the winter of 1995–1996. Biffle dominated the series championship that winter, leading former ESPN announcer and NASCAR champion, Benny Parsons, to recommend the driver to Jack Roush.[2]
Biffle entered the first two races of the 1996 Winston West Series, finishing 30th at Tucson and 4th at Altamont. His debut in one of NASCAR's national divisions came later that year when he ran the final two Busch Series races of the season. Driving a Chevrolet for Dick Bown, he finished 23rd at Rockingham but lost an engine the following race at Homestead and finished 36th. In 1997, Biffle competed in the now-defunct NASCAR Northwest Series and won the Most Popular Driver Award.[3]
Craftsman Truck Series[edit]
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Roush Racing promoted Biffle to a full-time driver in the Craftsman Truck Series in 1998. Despite not winning a race that season, Biffle's four pole positions are the most by a Truck Series rookie to date and they helped him earn an 8th-place finish in the final standings and the Rookie of the Year Award. He followed it up with a stellar 1999 season in which he recorded nine wins, a single-season Truck Series record that still stands as of 2018[update]. He finished second in the final standings, just eight points behind champion Jack Sprague.
In 2000, Biffle won the Truck Series title with another five-win season, beating his Roush teammate Kurt Busch by 230 points. It was Biffle's first championship in one of NASCAR's three major series. It was announced that Biffle would move up to the Busch Series for 2001; however, he ran four more Truck races for Roush that season and won at Phoenix. Biffle's last Truck Series start was in 2004 for another long-time Ford team, Circle Bar Racing, at Homestead.
Busch Series[edit]
Biffle joined the Busch Series full-time in 2001 and won the Rookie of the Year Award with five wins a fourth-place finish in the final standings. The following season, he won another four races and earned 20 top-five finishes out of 34 races en route to his first Busch Series title and the second NASCAR national championship of his career.
He ran only part-time in 2003 as Roush moved him up to a full-time ride in the Winston Cup Series for that season, but he returned to contend for the Busch Series championship again in 2004. He placed third in the standings behind Martin Truex, Jr. and Kyle Busch. From 2005 to 2009, Biffle raced part-time for Roush Fenway Racing in the Busch (now Xfinity Series) every year. He won twice in 2009, at Las Vegas and Phoenix, after going winless the previous two seasons. Biffle returned to the Nationwide Series in 2010, driving the #27 Ford for Baker Curb Racing.[4]
Cup Series[edit]
2008 Cup racecar
Biffle began his Cup Series career in the 2002 season. He attempted to qualify in a Roush Ford for the 2002 Daytona 500 but failed to make the race. He would make his first Cup debut nine races later at California, a race in which he finished 13th. That was his best finish in seven races that year as he also drove four in a Chevrolet for Andy Petree Racing and two in a Dodge for Petty Enterprises.
Biffle began competing full-time in NASCAR's top division in 2003, with a sponsorship from W. W. Grainger, who had previously sponsored him in the Busch and Truck Series. He earned his first win in the Pepsi 400 at Daytona that season and finished second to Jamie McMurray (who would later join him as a teammate at Roush) for Raybestos Rookie of the Year. Biffle placed 20th in the final points standings.
Biffle made an immediate impact in his sophomore season in 2004, earning the pole in the Daytona 500. However, Biffle was forced to start at the rear due to an engine change. Despite missing NASCAR's first-ever Chase for the NEXTEL Cup, Biffle won twice that season, at Michigan and Homestead en route to a 17th-place finish in the final points standings.
2005 was Biffle's breakout season. He won six races (at California Speedway, Texas, Darlington, Dover and Michigan along with the season finale at Homestead), the most of any driver that year, and qualified for the Chase for the first time in his career, bringing home a second-place finish in the standings, 35 points behind champion Tony Stewart; Biffle tied with his teammate Carl Edwards in points but won the tie-breaker based on race wins.
Biffle regressed in 2006, missing the Chase for the Cup despite winning twice at Darlington Raceway and Homestead-Miami Speedway (both of which were tracks at which he had also won in the previous season). He finished 13th in the standings, third-best of the drivers not to qualify for the Chase. He also missed the Chase the following year, in a season marred by the #16 team's new primary sponsor Ameriquest Mortgage suffering financial difficulty and having to sell off a number of its race sponsorships. Biffle won only one race in 2007, at Kansas Speedway. As Biffle was doing burnouts on the track, third place Jimmie Johnson and second place Clint Bowyer accused Biffle of not maintaining speed under a final lap caution but this was denied by NASCAR who said Biffle had pace car speed.[citation needed]
For 2007 Biffle finished 14th in the standings, second-best of the non-Chase drivers as the Chase expanded to a 12-driver format that year.
In June 2008, Biffle signed a year-long contract extension with Roush Fenway Racing.[5] Despite going winless during the 26-race regular season, Biffle made for the Chase for the Sprint Cup that year and won the first two Chase races, at New Hampshire and Dover. In doing so, he became the first driver to win the first two Chase races in a season.
Biffle qualified for the Chase for the second year in a row in 2009 but, for the first time since 2002 (when he ran a limited schedule), failed to record a win. During a test in January 2009 at Texas World Speedway, Biffle managed to reach 218 miles per hour (351 km/h) in a test for Roush Fenway Racing as part of evading NASCAR's testing ban. This became the fastest time ever achieved on this track by any competitor (amateur or professional).
In 2010 Biffle qualified for the third year in a row for the Chase despite spotty performance in the regular season. He won twice at Pocono and Kansas. For 2011, Biffle's season improved, thanks in part to the implementation of Ford's new FR9 engine. However, crew chief Greg Erwin was replaced after Kentucky by Matt Puccia. The addition of Puccia helped Biffle's performance late in the season, despite the team missing the Chase and finishing 16th in points. Biffle missed the Chase in 2011 for the first time since 2007.[6]
Biffle competes in the 2013 STP Gas Booster 500
In 2012 Biffle and Puccia remained at RFR, and gained the points lead after Las Vegas after three consecutive third-place finishes. At the 2012 Daytona 500, Biffle found himself second coming to the white flag for the third time in two years and again finished third. Eerily, the third place at Vegas came in Biffle's 333rd Cup start. Biffle's first win of the 2012 season came at Texas Motor Speedway in the Samsung Mobile 500 after passing Jimmie Johnson with 30 laps left in the race.[7] Biffle won at Michigan holding off Brad Keselowski after Jimmie Johnson blew an engine.[8]
Biffle started off 2013 by being in the same position for the third time in four years; in second place coming to the white flag in the 2013 Daytona 500 but this time ended up sixth. In the 2013 Quicken Loans 400 at Michigan, Biffle won his fourth race at the track and the 1,000th victory for Ford.[9][10]
At the 2014 Coca-Cola 600, Biffle surpassed Clint Bowyer's record for most consecutive races without failing to finish with 84, tying Herman Beam's record, dating back to the 2011 Ford 400. The following week at the FedEx 400, he broke Beam's record by finishing the race 108 laps down in 38th.[11] Later in the season, he finished with a DNF for the first time in 89 races after a wreck in the Coke Zero 400, finishing 29th.
Biffle racing at New Hampshire Motor Speedway in 2015
Biffle began the pre-season with an announcement that he would stay at Roush Fenway Racing to help the team. Biffle began 2015, with a 10th-place finish in the Daytona 500 with new primary sponsor, Ortho Bug-B-Gon. Unfortunately, that was as good as it could get for Biffle as he faded outside the top twenty in points. He struggled mightily before picking up a second-place finish in the 2015 Coca-Cola 600, after starting fourth. He went on to pick up a fifth-place finish at Pocono in the 2015 Windows 10 400 and a fourth-place at New Hampshire in the 2015 Sylvania 300, finishing twenty in points.
Ortho announced they would depart Roush following the 2015 season, leaving Biffle without a primary sponsor for the 2016 season. KFC then announced they would sponsor Biffle throughout speedweeks and in the Daytona 500. He earned his first pole position in four seasons during qualifying for the Coke Zero 400 at Daytona, and went on to finish eighth in the race.
After finishing 23rd in points in 2016, Biffle and Roush Fenway mutually parted ways, making Biffle a free agent for the upcoming 2017 season. He did not sign on with a ride for the 2017 season.[12] Biffle has remained inactive (driving) since leaving RFR.
Personal life[edit]
Biffle signs autographs along pit lane at Pocono Raceway
Greg is the son of Garland Jack Biffle II (1941-2016) and Sally Frye. He has a brother, Jeffrey. He is of German and English descent as his ancestor, Johannes Büffel (1728-1804) came from Contwig in Western Germany and settled in North Carolina.
Biffle married Nicole (née Lunders) on October 17, 2007.[13] Their daughter, Emma Elizabeth, was born on July 6, 2011. At birth, she weighed 7 lbs and 6 oz.[14] The couple separated in early 2015 and are now divorced as of early 2016.
Biffle is a fan of fishing and enjoys deep sea fishing in Mexico, where he keeps a factory sponsored Luhrs fishing boat. He formerly owned a pub in his hometown of Vancouver called "Biffle's Pub and Grill" located at 11500 NE 76th St. In 2010 Biffle announced that he had become part-owner of Willamette Speedway in Lebanon, Oregon along with Sunset Speedway in Banks, Oregon.[15] He is also a private pilot and owns a Cessna 210, along with a Dassault Falcon 50 with the tail number N116GB, a Dassault Falcon 10 with the tail number N316GB, and a Bell 206 with tail number N216GB.[16] Biffle owns a 2007 Ford GT and a 2007 Shelby Mustang GT500. The Shelby Mustang engine was rebuilt in 2013 and has 983 horsepower and 799 lb-ft of torque.[17]
Appearances in media[edit]
Biffle guest starred in a 2005 episode of CBS's situational comedy Yes, Dear entitled "On Your Marks, Get Set, Mow". He portrayed himself as a NASCAR racer moonlighting in a small-time lawnmower racing series.[citation needed]
Biffle appeared on a special features scene of the 2006 NASCAR-themed comedy film, Talladega Nights: The Ballad of Ricky Bobby, but was not credited with appearing in the film itself.[citation needed]
On December 22, 2007, Biffle appeared on the Food Network show Paula's Party with cook Paula Deen to cook steak,[18] and took Deen for a ride in his 2007 Ford Mustang Shelby GT500.[19]
Biffle was a regular panelist on the Speed program This Week in NASCAR.[20] He also appeared on an episode of Speed Network TV's show "Pass Time" filmed in 2009, he ran his Mustang GT500 in 10.11 seconds.[citation needed]
Biffle appeared in the 22nd episode of season 3 of American Restoration (entitled "Dirt Bike Duel"), where he brought in a 1970s Montessa off-road motorcycle.[21]
On February 17, 2017, Biffle announced that instead of racing full-time in 2017, he would join NBC Sports' NASCAR America as an analyst beginning March 1, 2017.[22]
Greg Biffle Foundation[edit]
Biffle also has a foundation in his name he managed. His primary goal is to create awareness and serve as an advocate to improve the well-being of animals by engaging the power and passion of the motorsports industry. The foundation donates to local Humane Societies, no-kill animal shelters, spay and neuter clinics and the Animal Adoption League.[23]
Motorsports career results[edit]
NASCAR[edit]
(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
Sprint Cup Series[edit]
NASCAR Sprint Cup Series results
Year
Team
No.
Make
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
NSCC
Pts
2002
Roush Racing
16
Ford
DAY
DNQ CAR LVS ATL DAR BRI TEX MAR TAL CAL
13 RCH CLT DOV POC MCH SON DAY CHI NHA POC IND GLN MCH
DNQ BRI DAR ATL
DNQ
48th
570
Andy Petree Racing
55
Chevy
RCH
33 NHA
27 DOV
33 KAN
36 TAL CLT MAR
Petty Enterprises
44
Dodge
CAR
25 PHO HOM
25
2003
Roush Racing
16
Ford
DAY
21 CAR
22 LVS
DNQ ATL
13 DAR
12 BRI
5 TEX
28 TAL
22 MAR
18 CAL
18 RCH
17 CLT
16 DOV
30 POC
20 MCH
31 SON
37 DAY
1 CHI
20 NHA
10 POC
27 IND
21 GLN
30 MCH
4 BRI
22 DAR
10 RCH
20 NHA
43 DOV
7 TAL
24 KAN
12 CLT
17 MAR
19 ATL
34 PHO
15 CAR
11 HOM
35
20th
3696
2004
DAY
12 CAR
23 LVS
40 ATL
8 DAR
12 BRI
12 TEX
31 MAR
35 TAL
15 CAL
33 RCH
21 CLT
21 DOV
26 POC
11 MCH
23 SON
13 DAY
31 CHI
20 NHA
35 POC
4 IND
6 GLN
35 MCH
1 BRI
11 CAL
36 RCH
8 NHA
28 DOV
11 TAL
28 KAN
3 CLT
33 MAR
17 ATL
10 PHO
13 DAR
24 HOM
1
17th
3902
2005
DAY
25 CAL
1 LVS
6 ATL
3 BRI
9 MAR
29 TEX
1 PHO
41 TAL
13 DAR
1 RCH
6 CLT
6 DOV
1 POC
30 MCH
1 SON
14 DAY
36 CHI
11 NHA
5 POC
17 IND
21 GLN
38 MCH
6 BRI
3 CAL
2 RCH
3 NHA
4 DOV
13 TAL
27 KAN
2 CLT
3 MAR
20 ATL
7 TEX
20 PHO
2 HOM
1
2nd
6498
2006
DAY
31 CAL
42* LVS
8 ATL
16* BRI
7 MAR
31 TEX
42 PHO
15* TAL
38 RCH
4 DAR
1* CLT
7 DOV
8 POC
6 MCH
4 SON
4 DAY
31 CHI
11 NHA
3 POC
24 IND
33 GLN
38 MCH
7 BRI
19 CAL
24 RCH
6 NHA
14 DOV
5 KAN
12 TAL
41 CLT
37 MAR
32 ATL
5 TEX
35 PHO
34 HOM
1
13th
4075
2007
Roush Fenway Racing
DAY
25 CAL
15 LVS
16 ATL
41 BRI
5 MAR
32 TEX
6 PHO
17 TAL
29 RCH
19 DAR
15 CLT
43 DOV
6 POC
30 MCH
38 SON
5 NHA
31 DAY
6 CHI
11 IND
15 POC
23 GLN
10 MCH
19 BRI
10 CAL
17 RCH
39 NHA
13 DOV
2 KAN
1 TAL
23 CLT
27 MAR
7 ATL
22 TEX
33 PHO
2 HOM
13
14th
3991
2008
DAY
10 CAL
15 LVS
3 ATL
4 BRI
4 MAR
20 TEX
39 PHO
9 TAL
18 RCH
14 DAR
43 CLT
2 DOV
3* POC
15 MCH
20 SON
11 NHA
21 DAY
43 CHI
4 IND
8 POC
13 GLN
21 MCH
4 BRI
11 CAL
2 RCH
14 NHA
1 DOV
1 KAN
3 TAL
24 CLT
7 MAR
12 ATL
10 TEX
5 PHO
11 HOM
18
3rd
6467
2009
DAY
20 CAL
4 LVS
7 ATL
34 BRI
39 MAR
28 TEX
3 PHO
5 TAL
7 RCH
17 DAR
8 CLT
20 DOV
3 POC
11 MCH
5 SON
28 NHA
18 DAY
18 CHI
31 IND
4 POC
15 GLN
5 MCH
20 BRI
4 ATL
10 RCH
13 NHA
9 DOV
13 KAN
3 CAL
20 CLT
16 MAR
25 TAL
4 TEX
8 PHO
14 HOM
14
7th
6292
2010
DAY
3 CAL
10 LVS
10 ATL
8 BRI
4 MAR
10 PHO
22 TEX
10 TAL
17 RCH
22 DAR
22 DOV
6 CLT
32 POC
28 MCH
9 SON
7 NHA
16 DAY
20 CHI
35 IND
3 POC
1 GLN
24 MCH
4 BRI
8 ATL
36 RCH
32 NHA
17 DOV
19 KAN
1 CAL
41 CLT
5 MAR
33 TAL
19 TEX
5 PHO
4 HOM
10
6th
6247
2011
DAY
35 PHO
20 LVS
28 BRI
8 CAL
11 MAR
21 TEX
4 TAL
7 RCH
15 DAR
8 DOV
19 CLT
13 KAN
10 POC
27 MCH
15 SON
23 DAY
18 KEN
21 NHA
18 IND
7 POC
8 GLN
31 MCH
20 BRI
31 ATL
12 RCH
13 CHI
26 NHA
3 DOV
27 KAN
8 CLT
15 TAL
14 MAR
15 TEX
5 PHO
13 HOM
35
16th
997
2012
DAY
3 PHO
3 LVS
3 BRI
13 CAL
6 MAR
13 TEX
1 KAN
5 RCH
18 TAL
5 DAR
12 CLT
4 DOV
11 POC
24 MCH
4 SON
7 KEN
21 DAY
21 NHA
9 IND
3 POC
15 GLN
6 MCH
1 BRI
19 ATL
15 RCH
9 CHI
13 NHA
18 DOV
16 TAL
6 CLT
4 KAN
27 MAR
10 TEX
10 PHO
7 HOM
5
5th
2332
2013
DAY
6 PHO
17 LVS
17 BRI
11 CAL
6 MAR
9 TEX
4 KAN
19 RCH
36 TAL
36 DAR
13 CLT
31 DOV
15 POC
2 MCH
1 SON
8 KEN
34 DAY
17 NHA
15 IND
24 POC
10 GLN
16 MCH
9 BRI
9 ATL
15 RCH
12 CHI
16 NHA
3 DOV
9 KAN
13 CLT
16 TAL
11 MAR
9 TEX
12 PHO
13 HOM
24
9th
2321
2014
DAY
8 PHO
17 LVS
22 BRI
12 CAL
40 MAR
18 TEX
6 DAR
5 RCH
15 TAL
2* KAN
16 CLT
21 DOV
38 POC
16 MCH
20 SON
9 KEN
14 DAY
29 NHA
15 IND
13 POC
5 GLN
8 MCH
10 BRI
10 ATL
10 RCH
19 CHI
23 NHA
16 DOV
21 KAN
15 CLT
18 TAL
25 MAR
13 TEX
13 PHO
9 HOM
41
14th
2247
2015
DAY
10 ATL
25 LVS
14 PHO
27 CAL
32 MAR
19 TEX
17 BRI
30 RCH
21 TAL
37 KAN
12 CLT
2 DOV
17 POC
12 MCH
36 SON
27 DAY
20 KEN
16 NHA
27 IND
19 POC
5 GLN
14 MCH
23 BRI
25 DAR
18 RCH
31 CHI
21 NHA
4 DOV
13 CLT
24 KAN
17 TAL
20 MAR
26 TEX
19 PHO
25 HOM
16
20th
869
2016
DAY
34 ATL
13 LVS
20 PHO
21 CAL
37 MAR
12 TEX
39 BRI
12 RCH
14 TAL
20 KAN
27 DOV
29 CLT
11 POC
26 MCH
19 SON
18 DAY
8 KEN
6 NHA
5 IND
39 POC
25 GLN
39 BRI
16 MCH
11 DAR
36 RCH
23 CHI
26 NHA
33 DOV
18 CLT
35 KAN
25 TAL
15 MAR
13 TEX
18 PHO
16 HOM
17
23rd
691
Daytona 500[edit]
Year
Team
Manufacturer
Start
Finish
2002 Roush Racing Ford DNQ
2003 27 21
2004 1 12
2005 23 25
2006 16 31
2007 Roush Fenway Racing 25 25
2008 18 10
2009 35 20
2010 23 3
2011 26 35
2012 2 3
2013 5 6
2014 25 8
2015 8 10
2016 15 34
Nationwide Series[edit]
NASCAR Nationwide Series results
Year
Team
No.
Make
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
NNSC
Pts
1996
Bown Racing
51
Chevy
DAY CAR RCH ATL NSV DAR BRI HCY NZH CLT DOV SBO MYB GLN MLW NHA TAL IRP MCH BRI DAR RCH DOV CLT CAR
23 HOM
36
75th
149
1999
Team Yellow Racing
19
Chevy
DAY CAR LVS ATL DAR TEX NSV BRI TAL CAL NHA RCH NZH CLT DOV SBO GLN MLW MYB PPR GTY IRP MCH BRI DAR RCH DOV CLT CAR
DNQ MEM PHO HOM
NA
-
2001
Roush Racing
60
Ford
DAY
22 CAR
3 LVS
2 ATL
2 DAR
11 BRI
30 TEX
7 NSH
1* TAL
9 CAL
6 RCH
37 NHA
11 NZH
1* CLT
6 DOV
9 KEN
2 MLW
1 GLN
2 CHI
39 GTY
4 PPR
5 IRP
2 MCH
43 BRI
18 DAR
15 RCH
35 DOV
5 KAN
3 CLT
1 MEM
20 PHO
1* CAR
12 HOM
3
4th
4509
2002
DAY
22 CAR
2 LVS
9 DAR
2 BRI
5 TEX
17 NSH
33 TAL
26 CAL
10 RCH
3 NHA
31 NZH
27 CLT
2 DOV
1 NSH
3 KEN
2 MLW
1 DAY
2 CHI
8 GTY
1 PPR
2 IRP
1 MCH
42 BRI
3 DAR
4 RCH
6 DOV
17 KAN
4 CLT
6 MEM
34 ATL
5 CAR
2 PHO
3 HOM
4
1st
4924
2003
9
DAY CAR LVS DAR BRI TEX TAL NSH CAL RCH GTY NZH CLT
12 DOV NSH KEN MLW
35th
1502
Evans Motorsports
7
Pontiac
DAY
23 CHI NHA PPR IRP
Chevy
MCH
21 BRI
38 DAR
29 RCH
28 DOV
11 KAN
3 CLT
1 MEM
39 ATL
1* PHO
10 CAR
11 HOM
13
2004
Roush Racing
60
Ford
DAY
11 CAR
38 LVS
10 DAR
1 BRI
4 TEX
34 NSH
40 TAL
21 CAL
1 GTY
7 RCH
2 NZH
32 CLT
6 DOV
1 NSH
13 KEN
2 MLW
7 DAY
2 CHI
32 NHA
30 PPR
1 IRP
5 MCH
8 BRI
33 CAL
1 RCH
11 DOV
14 KAN
2 CLT
4 MEM
2 ATL
5 PHO
5 DAR
37 HOM
10
3rd
4568
2005
Brewco Motorsports
66
Ford
DAY
8 CAL
40 MXC LVS
5 ATL
6 NSH BRI
10 TEX
2 PHO
1* TAL
36 DAR
4 RCH
5 CLT
4 DOV
8 NSH KEN
30 MLW DAY
3 CHI
2 NHA
31 PPR GTY IRP GLN
12 MCH
2 BRI
2 CAL
2 RCH
10 DOV
5 KAN
2 CLT
36 MEM TEX
2 PHO
5 HOM
2
10th
3865
2006
Roush Racing
16
Ford
DAY
31 CAL
1 MXC LVS
4 ATL
3 BRI
28 TEX
2 NSH PHO
6 TAL
6 RCH
4 DAR
5 CLT
12 DOV
8 DAY
9 CHI
24 NHA
10 IRP
4 MCH
43 BRI
37 CAL
23 RCH
2 DOV
8 KAN
8 CLT
41 MEM TEX
23 PHO
12 HOM
38
9th
3789
Brewco Motorsports
66
Ford
NSH
7 KEN
17 MLW MAR
4 GTY GLN
4
2007
Roush Fenway Racing
26
Ford
DAY
10
9th
3466
16
CAL
5 LVS
38 TEX
36 TAL
30 RCH
6 CLT
21 DOV
18 DAY
37 CHI
39 GTY IRP
2 MCH
5 CAL
32 RCH
13 DOV
9 KAN
10 CLT
30 MEM TEX
16 PHO
36 HOM
6
Brewco Motorsports
37
Ford
MXC
20 ATL
40 BRI
7 NSH PHO
6 DAR
8 NSH
28 KEN
10 MLW NHA
7 CGV
20 GLN
11 BRI
14
2008
Roush Fenway Racing
16
Ford
DAY
7 CAL LVS
2 BRI
13 NSH TEX PHO MXC TAL
11 RCH DAR CLT
7 DOV
5 NSH
10 KEN MLW NHA
19 DAY CHI
6 GTY IRP CGV
8 GLN MCH
5 BRI
3 CAL RCH
6 DOV KAN
18 CLT MEM TEX PHO HOM
25th
2092
Brewco Motorsports
37
Ford
ATL
21
2009
Roush Fenway Racing
16
Ford
DAY
5 CAL
34 LVS
1* BRI TEX NSH PHO
1* TAL RCH DAR CLT
12 DOV
25 NSH KEN MLW NHA
7 DAY CHI
7 GTY IRP IOW GLN
7 MCH
8 BRI CGV ATL
8 RCH
12 DOV KAN
5 CAL
14 CLT MEM TEX PHO HOM
24th
1966
2010
Baker Curb Racing
27
Ford
DAY
26 CAL
2 LVS
9 BRI
6 NSH PHO
5 TEX
7 TAL RCH
2 DAR
35 DOV
8 CLT
13 NSH KEN ROA NHA DAY CHI GTY IRP IOW GLN MCH BRI CGV ATL RCH DOV KAN CAL CLT GTY TEX PHO HOM
35th
1368
Craftsman Truck Series[edit]
NASCAR Craftsman Truck Series results
Year
Team
No.
Make
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
NCTC
Pts
1998
Roush Racing
80
Ford
WDW
5
8th
3872
50
HOM
4 PHO
36 POR
26 EVG
17 I70
21 GLN
27 TEX
22 BRI
29 MLW
5 NZH
30 CAL
7 PPR
17 IRP
7 NHA
2 FLM
24 NSV
4 HPT
21 LVL
8 RCH
3 MEM
22 GTY
19 MAR
8 SON
20 MMR
14 PHO
2 LVS
5
1999
HOM
11 PHO
11 EVG
10 MMR
24 MAR
5 MEM
1 PPR
14 I70
10 BRI
9 TEX
3 PIR
1 GLN
4 MLW
1 NSV
22 NZH
1 MCH
1 NHA
4 IRP
1 GTY
1 HPT
8 RCH
1 LVS
1 LVL
14 TEX
2 CAL
7
2nd
3739
2000
DAY
11 HOM
5 PHO
5 MMR
12 MAR
14 PIR
13 GTY
4 MEM
2 PPR
1 EVG
4 TEX
1 KEN
1 GLN
1 MLW
3 NHA
4 NZH
3 MCH
1 IRP
5 NSV
14 CIC
2 RCH
2 DOV
2 TEX
25 CAL
5
1st
3826
2001
99
DAY HOM MMR MAR GTY DAR PPR DOV TEX MEM
9 MLW KAN KEN NHA IRP NSH
7 CIC NZH
1 RCH SBO TEX LVS PHO
1 CAL
41st
664
2004
Circle Bar Racing
44
Ford
DAY ATL MAR MFD CLT DOV TEX MEM MLW KAN KEN GTW MCH IRP NSH BRI RCH NHA LVS CAL TEX MAR PHO DAR HOM
8
77th
142
* Season still in progress.
** Not factored into total
International Race of Champions[edit]
(key) (Bold – Pole position. * – Most laps led.)
International Race of Champions results
Season
Make
1
2
3
4
Pos.
Points
2003
Pontiac
DAY
5 TAL
3 CHI
6 IND
7
7th
41
24 Hours of Daytona[edit]
(key)
24 Hours of Daytona results
Year
Class
No
Team
Car
Co-drivers
Laps
Position
Class Pos.
2005
DP 49 Multimatic Motorsports Ford Multimatic DP Scott Maxwell
Kurt Busch
Matt Kenseth 588 27 DNF 15 DNF
See also[edit]
List of all-time NASCAR Cup Series winners
List of animal rights advocates
List of Daytona 500 pole position winners
List of NASCAR Camping World Truck Series champions
List of NASCAR drivers who have won in each of top three series
List of NASCAR Nationwide Series champions
List of NASCAR Sprint All-Star Race drivers
List of people from Washington (state)
Animal rights portal
Biography portal
NASCAR portal
Washington portal
References[edit]
Jump up ^ http://nationwide.nascar.com/nationwide-series/drivers/dps/gbiffle00 Archived February 14, 2010, at the Wayback Machine.
Jump up ^ "Greg Biffle". Archived from the original on September 27, 2007. Retrieved June 21, 2013.
Jump up ^ "Greg Biffle Profile". Racingone.com. Retrieved June 21, 2013.
Jump up ^ "Biffle back at Baker Curb, will drive No. 27 Ford". NASCAR.com. January 9, 2010. Archived from the original on January 12, 2010. Retrieved June 21, 2013.
Jump up ^ "Biffle signs 3-year extension with Roush Fenway". Gnextinc.com. Archived from the original on June 4, 2011. Retrieved June 21, 2013.
Jump up ^ "Year in Review: Slow start in Chase cost Biffle chance at winning championship". NASCAR.com. December 12, 2012. Retrieved November 23, 2014.
Jump up ^ Jensen, Tom (April 14, 2012). "CUP: Biffle Makes Late Charge To Victory". Speedtv.com. Archived from the original on April 17, 2012. Retrieved April 14, 2012.
Jump up ^ "Greg Biffle captures win at Michigan". ESPN. August 21, 2012. Retrieved 2013-08-29.
Jump up ^ Held, Scott (June 16, 2013). "Biffle emerges late, lands Michigan victory". NASCAR. Retrieved June 16, 2013.
Jump up ^ Ryan, Nate (June 16, 2013). "Greg Biffle wins in Michigan, balance of power shifting". USA Today. Retrieved June 20, 2013.
Jump up ^ Long, Dustin (May 27, 2014). "NASCAR Notebook: A Look At Who Is Testing Where". Motor Racing Network. Retrieved May 29, 2014.
Jump up ^ Gluck, Jeff (November 22, 2016). "Greg Biffle departs Roush Fenway Racing after 19 seasons". USA Today. Retrieved November 29, 2016.
Jump up ^ "Michigan Ann Arbor Bay City Detroit Flint Grand Rapids Jackson Kalamazoo Lansing Muskegon Saginaw All Michigan". Mlive.com. November 1, 2011. Archived from the original on April 7, 2014. Retrieved June 21, 2013.
Jump up ^ "Greg Biffle, Wife Nicole Welcome Baby Daughter Emma Elizabeth". Sbnation.com. July 6, 2011. Retrieved November 23, 2014.
Jump up ^ "Greg Biffle becomes part-owner of Oregon dirt track - ESPN". ESPN.com.
Jump up ^ Marsh, Alton K. (March 1, 2009). "NASCAR drivers fly, too — Aircraft Owners and Pilots Association". Aopa.org. Retrieved June 21, 2013. [permanent dead link]
Jump up ^ "Greg Biffle's 2008 SHELBY Mustang GT500". December 31, 2013. Retrieved December 31, 2013.
Jump up ^ Greg Biffle cooks steak with Paula Deen.[dead link]
Jump up ^ Greg Biffle doing donuts with Paula Deen[dead link]
Jump up ^ Arneson, Erik (February 8, 2008). "SPEED Puts Familiar Faces in New Places". Speed. Archived from the original on June 24, 2013. Retrieved June 20, 2013.
Jump up ^ Hoppes, Lynn (June 6, 2012). "Greg Biffle is on 'American Restoration'". ESPN. Retrieved June 20, 2013.
Jump up ^ "Greg Biffle won't participate full-time in NASCAR in 2017 | FOX Sports". FOX Sports. 2017-02-17. Retrieved 2017-02-17.
Jump up ^ "About the Greg Biffle Foundation". Greg Biffle Foundation. Archived from the original on June 20, 2013. Retrieved June 20, 2013.
External links[edit]
Official website
Greg Biffle driver statistics at Racing-Reference
Greg Biffle at Roush Fenway Racing
The Greg Biffle Foundation
Sporting positions
Preceded by
Kevin Harvick NASCAR Busch Series Champion
2002 Succeeded by
Brian Vickers
Preceded by
Jack Sprague NASCAR Craftsman Truck Series Champion
2000 Succeeded by
Jack Sprague
Achievements
Preceded by
Kevin Harvick NASCAR Busch Series Rookie of the Year
2001 Succeeded by
Scott Riggs
Preceded by
Kenny Irwin, Jr. Craftsman Truck Series Rookie of the Year
1998 Succeeded by
Mike Stefanik
show
v
t
e
Xfinity Series Drivers' Champions
1982 J. Ingram
1983 S. Ard
1984 S. Ard
1985 J. Ingram
1986 L. Pearson
1987 L. Pearson
1988 T. Ellis
1989 R. Moroso
1990 C. Bown
1991 B. Labonte
1992 J. Nemechek
1993 S. Grissom
1994 D. Green
1995 J. Benson Jr.
1996 R. LaJoie
1997 R. LaJoie
1998 D. Earnhardt Jr.
1999 D. Earnhardt Jr.
2000 J. Green
2001 K. Harvick
2002 G. Biffle
2003 B. Vickers
2004 M. Truex Jr.
2005 M. Truex Jr.
2006 K. Harvick
2007 C. Edwards
2008 C. Bowyer
2009 K. Busch
2010 B. Keselowski
2011 R. Stenhouse Jr.
2012 R. Stenhouse Jr.
2013 A. Dillon
2014 C. Elliott
2015 C. Buescher
2016 D. Suárez
2017 W. Byron
show
v
t
e
Camping World Truck Series Drivers' Champions
1995 M. Skinner
1996 R. Hornaday Jr.
1997 J. Sprague
1998 R. Hornaday Jr.
1999 J. Sprague
2000 G. Biffle
2001 J. Sprague
2002 M. Bliss
2003 T. Kvapil
2004 B. Hamilton
2005 T. Musgrave
2006 T. Bodine
2007 R. Hornaday Jr.
2008 J. Benson Jr.
2009 R. Hornaday Jr.
2010 T. Bodine
2011 A. Dillon
2012 J. Buescher
2013 M. Crafton
2014 M. Crafton
2015 E. Jones
2016 J. Sauter
2017 C. Bell
show
v
t
e
Roush Fenway Racing
Personnel
Jack Roush
John W. Henry
Sam Belnavis
Geoff Smith
Steve Newmark
Robbie Reiser
Drivers
Monster Energy Cup Series
(6) Trevor Bayne / Matt Kenseth
(17) Ricky Stenhouse Jr.
Xfinity Series
(6) Conor Daly
(16) Ryan Reed
(60) Chase Briscoe / Austin Cindric / Ty Majeski
Grand-Am CTSCC
(61) Jack Roush Jr.
Crew chiefs
Cup Series
(6) Matt Puccia
(17) Brian Pattie
Xfinity Series
(6) Phil Gould
(16) Mike Kelley
Development drivers
Kyle Benjamin
Gray Gaulding
Ty Majeski
Kyle Weatherman
Notable former drivers
NASCAR
Stanton Barrett
T. J. Bell
Johnny Benson Jr.
Greg Biffle
Mike Bliss
Chuck Bown
Colin Braun
Chris Buescher
Jeff Burton
Kurt Busch
Ricky Craven
Erik Darnell
Wally Dallenbach Jr.
Carl Edwards
Nathan Haseleu
Billy Johnson
Todd Kluever
Travis Kvapil
Kevin Lepage
Chad Little
Mark Martin
Jamie McMurray
Paul Menard
Ted Musgrave
Danny O'Quinn
Travis Pastrana
David Ragan
Elliott Sadler
Joe Ruttman
Darrell Wallace Jr.
Jon Wood
Trans-Am
Wally Dallenbach Jr.
Pete Halsmer
Tommy Kendall
Scott Pruett
Willy T. Ribbs
Dorsey Schroeder
NASCAR Cup Championships
2003 (Kenseth)
2004 (Ku. Busch)
NASCAR Xfinity Series Championships
2002 (Biffle)
2007 (Edwards)
2011 (Stenhouse)
2012 (Stenhouse)
2015 (Buescher)
NASCAR Truck Series Championships
2000 (Biffle)
Daytona 500 wins
2009 (Kenseth)
2012 (Kenseth)
Coca-Cola 600 wins
1999 (J. Burton)
2000 (Kenseth)
2001 (J. Burton)
2002 (Martin)
Southern 500 wins
1993 (Martin)
1999 (J. Burton)
2005 (Biffle)
2006 (Biffle)
All-Star Race wins
1998 (Martin)
2004 (Kenseth)
2005 (Martin)
Partnerships and affiliations
Front Row Motorsports
Go Fas Racing
Roulo Brothers Racing
Stewart-Haas Racing
Team Penske
Wood Brothers Racing
See Also
Fenway Sports Group
Fenway Sports Management
Roush Performance
Roush Racing: Driver X
Roush-Yates Engines
show
v
t
e
NASCAR Rookies of the Year
Monster Energy Cup
1954: Pitt
1957: Rush
1958: Rollins
1959: R. Petty
1960: D. Pearson
1961: Wilson
1962: Cox
1963: Wade
1964: Cooper
1965: McQuagg
1966: Hylton
1967: Do. Allison
1968: P. Hamilton
1969: Brooks
1970: Dennis
1971: Ballard
1972: L. Smith
1973: Pond
1974: Ross
1975: B. Hill
1976: Manning
1977: Rudd
1978: Thomas
1979: Earnhardt
1980: Ridley
1981: R. Bouchard
1982: G. Bodine
1983: Marlin
1984: R. Wallace
1985: Schrader
1986: Kulwicki
1987: Da. Allison
1988: K. Bouchard
1989: Trickle
1990: Moroso
1991: B. Hamilton
1992: Hensley
1993: Gordon
1994: J. Burton
1995: Craven
1996: Benson
1997: Skinner
1998: Irwin
1999: Stewart
2000: Kenseth
2001: Harvick
2002: Newman
2003: McMurray
2004: Kahne
2005: Ky. Busch
2006: Hamlin
2007: Montoya
2008: R. Smith
2009: Logano
2010: Conway
2011: Lally
2012: Leicht
2013: Stenhouse Jr.
2014: K. Larson
2015: B. Moffitt
2016: C. Elliott
2017: E. Jones
Xfinity Series
1989: K. Wallace
1990: Nemechek
1991: J. Gordon
1992: Craven
1993: H. Sadler
1994: Benson
1995: Fuller
1996: G. Allen Jr.
1997: Park
1998: Santerre
1999: Raines
2000: Harvick
2001: Biffle
2002: Riggs
2003: Stremme
2004: Ky. Busch
2005: C. Edwards
2006: O'Quinn Jr.
2007: Ragan
2008: Cassill
2009: Allgaier
2010: Stenhouse Jr.
2011: T. Hill
2012: A. Dillon
2013: K. Larson
2014: C. Elliott
2015: D. Suárez
2016: E. Jones
2017: W. Byron
Camping World Truck
1996: Reffner
1997: Irwin
1998: Biffle
1999: Stefanik
2000: Ku. Busch
2001: Kvapil
2002: Gaughan
2003: C. Edwards
2004: Reutimann
2005: Kluever
2006: Darnell
2007: W. Allen
2008: Braun
2009: Jo. Sauter
2010: A. Dillon
2011: Coulter
2012: T. Dillon
2013: R. Blaney
2014: B. Kennedy
2015: E. Jones
2016: W. Byron
2017: C. Briscoe
show
v
t
e
NASCAR Triple Threats (Race Wins In All Three Major Series)
Dates listed are when the driver accomplished the "Triple Threat"
1990s
Ken Schrader (April 15, 1995)
Terry Labonte (September 7, 1995)
Mark Martin (September 28, 1996)
2000s
Bobby Hamilton (April 10, 2000)
Kevin Harvick (November 8, 2002)
Greg Biffle (July 5, 2003)
Jimmy Spencer (September 13, 2003)
Jamie McMurray (October 23, 2004)
Tony Stewart (February 19, 2005)
Steve Park (February 25, 2005)
Carl Edwards (March 20, 2005)
Bobby Labonte (April 9, 2005)
Kasey Kahne (May 14, 2005)
Kyle Busch (September 4, 2005)
Ricky Craven (October 22, 2005)
Kurt Busch (April 8, 2006)
Johnny Benson Jr. (June 17, 2006)
Clint Bowyer (September 16, 2007)
Ryan Newman (October 25, 2008)
David Reutimann (May 25, 2009)
2010s
Elliott Sadler (July 31, 2010)
Michael Waltrip (February 18, 2011)
Denny Hamlin (October 29, 2011)
Aric Almirola (July 6, 2014)
Brad Keselowski (August 21, 2014)
Joey Logano (March 28, 2015)
Kyle Larson (August 28, 2016)
Austin Dillon (May 28, 2017)
Ryan Blaney (June 11, 2017)
Authority control
WorldCat Identities
LCCN: n2006096079
VIAF: 9283294
Retrieved from "https://en.wikipedia.org/w/index.php?title=Greg_Biffle&oldid=843961238"
Categories:
Living people
1969 births
Sportspeople from Vancouver, Washington
Racing drivers from Washington (state)
24 Hours of Daytona drivers
NASCAR drivers
NASCAR Xfinity Series champions
NASCAR Truck Series champions
International Race of Champions drivers
3M people
People from Camas, Washington
20th-century American racing drivers
21st-century American racing drivers
Motorsport announcers
Hidden categories:
Webarchive template wayback links
All articles with dead external links
Articles with dead external links from September 2017
Articles with permanently dead external links
Articles with dead external links from April 2015
Use mdy dates from June 2013
Articles needing additional references from May 2017
All articles needing additional references
BLP articles lacking sources from September 2016
All BLP articles lacking sources
Articles containing potentially dated statements from 2018
All articles containing potentially dated statements
All articles with unsourced statements
Articles with unsourced statements from September 2016
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Parallel (geometry)
From Wikipedia, the free encyclopedia
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This article is about a mathematical relationship between lines. For other uses, see Parallel (disambiguation).
"Parallel lines" redirects here. For other uses, see Parallel lines (disambiguation).
Line art drawing of parallel lines and curves.
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. However, two lines in three-dimensional space which do not meet must be in a common plane to be considered parallel; otherwise they are called skew lines. Parallel planes are planes in the same three-dimensional space that never meet.
Parallel lines are the subject of Euclid's parallel postulate.[1] Parallelism is primarily a property of affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines can have analogous properties that are referred to as parallelism.
Contents
[hide]
1 Symbol
2 Euclidean parallelism
2.1 Two lines in a plane
2.1.1 Conditions for parallelism
2.1.2 History
2.1.3 Construction
2.1.4 Distance between two parallel lines
2.2 Two lines in three-dimensional space
2.3 A line and a plane
2.4 Two planes
3 Extension to non-Euclidean geometry
3.1 Hyperbolic geometry
3.2 Spherical or elliptic geometry
4 Reflexive variant
5 See also
6 Notes
7 References
8 Further reading
9 External links
Symbol[edit]
The parallel symbol is ∥ {\displaystyle \parallel } . For example, A B ∥ C D {\displaystyle AB\parallel CD} indicates that line AB is parallel to line CD.
In the Unicode character set, the "parallel" and "not parallel" signs have codepoints U+2225 (∥) and U+2226 (∦), respectively. In addition, U+22D5 (⋕) represents the relation "equal and parallel to".[2]
Euclidean parallelism[edit]
Two lines in a plane[edit]
Conditions for parallelism[edit]
As shown by the tick marks, lines a and b are parallel. This can be proved because the transversal t produces congruent corresponding angles θ {\displaystyle \theta } , shown here both to the right of the transversal, one above and adjacent to line a and the other above and adjacent to line b.
Given parallel straight lines l and m in Euclidean space, the following properties are equivalent:
Every point on line m is located at exactly the same (minimum) distance from line l (equidistant lines).
Line m is in the same plane as line l but does not intersect l (recall that lines extend to infinity in either direction).
When lines m and l are both intersected by a third straight line (a transversal) in the same plane, the corresponding angles of intersection with the transversal are congruent.
Since these are equivalent properties, any one of them could be taken as the definition of parallel lines in Euclidean space, but the first and third properties involve measurement, and so, are "more complicated" than the second. Thus, the second property is the one usually chosen as the defining property of parallel lines in Euclidean geometry.[3] The other properties are then consequences of Euclid's Parallel Postulate. Another property that also involves measurement is that lines parallel to each other have the same gradient (slope).
History[edit]
The definition of parallel lines as a pair of straight lines in a plane which do not meet appears as Definition 23 in Book I of Euclid's Elements.[4] Alternative definitions were discussed by other Greeks, often as part of an attempt to prove the parallel postulate. Proclus attributes a definition of parallel lines as equidistant lines to Posidonius and quotes Geminus in a similar vein. Simplicius also mentions Posidonius' definition as well as its modification by the philosopher Aganis.[4]
At the end of the nineteenth century, in England, Euclid's Elements was still the standard textbook in secondary schools. The traditional treatment of geometry was being pressured to change by the new developments in projective geometry and non-Euclidean geometry, so several new textbooks for the teaching of geometry were written at this time. A major difference between these reform texts, both between themselves and between them and Euclid, is the treatment of parallel lines.[5] These reform texts were not without their critics and one of them, Charles Dodgson (a.k.a. Lewis Carroll), wrote a play, Euclid and His Modern Rivals, in which these texts are lambasted.[6]
One of the early reform textbooks was James Maurice Wilson's Elementary Geometry of 1868.[7] Wilson based his definition of parallel lines on the primitive notion of direction. According to Wilhelm Killing[8] the idea may be traced back to Leibniz.[9] Wilson, without defining direction since it is a primitive, uses the term in other definitions such as his sixth definition, "Two straight lines that meet one another have different directions, and the difference of their directions is the angle between them." Wilson (1868, p. 2) In definition 15 he introduces parallel lines in this way; "Straight lines which have the same direction, but are not parts of the same straight line, are called parallel lines." Wilson (1868, p. 12) Augustus De Morgan reviewed this text and declared it a failure, primarily on the basis of this definition and the way Wilson used it to prove things about parallel lines. Dodgson also devotes a large section of his play (Act II, Scene VI § 1) to denouncing Wilson's treatment of parallels. Wilson edited this concept out of the third and higher editions of his text.[10]
Other properties, proposed by other reformers, used as replacements for the definition of parallel lines, did not fare much better. The main difficulty, as pointed out by Dodgson, was that to use them in this way required additional axioms to be added to the system. The equidistant line definition of Posidonius, expounded by Francis Cuthbertson in his 1874 text Euclidean Geometry suffers from the problem that the points that are found at a fixed given distance on one side of a straight line must be shown to form a straight line. This can not be proved and must be assumed to be true.[11] The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, The Elements of Geometry, simplified and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.
Construction[edit]
The three properties above lead to three different methods of construction[12] of parallel lines.
The problem: Draw a line through a parallel to l.
Property 1: Line m has everywhere the same distance to line l.
Property 2: Take a random line through a that intersects l in x. Move point x to infinity.
Property 3: Both l and m share a transversal line through a that intersect them at 90°.
Distance between two parallel lines[edit]
Main article: Distance between two lines
Because parallel lines in a Euclidean plane are equidistant there is a unique distance between the two parallel lines. Given the equations of two non-vertical, non-horizontal parallel lines,
y = m x + b 1 {\displaystyle y=mx+b_{1}\,}
y = m x + b 2 , {\displaystyle y=mx+b_{2}\,,}
the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m, a common perpendicular would have slope −1/m and we can take the line with equation y = −x/m as a common perpendicular. Solve the linear systems
{ y = m x + b 1 y = − x / m {\displaystyle {\begin{cases}y=mx+b_{1}\\y=-x/m\end{cases}}}
and
{ y = m x + b 2 y = − x / m {\displaystyle {\begin{cases}y=mx+b_{2}\\y=-x/m\end{cases}}}
to get the coordinates of the points. The solutions to the linear systems are the points
( x 1 , y 1 ) = ( − b 1 m m 2 + 1 , b 1 m 2 + 1 ) {\displaystyle \left(x_{1},y_{1}\right)\ =\left({\frac {-b_{1}m}{m^{2}+1}},{\frac {b_{1}}{m^{2}+1}}\right)\,}
and
( x 2 , y 2 ) = ( − b 2 m m 2 + 1 , b 2 m 2 + 1 ) . {\displaystyle \left(x_{2},y_{2}\right)\ =\left({\frac {-b_{2}m}{m^{2}+1}},{\frac {b_{2}}{m^{2}+1}}\right).}
These formulas still give the correct point coordinates even if the parallel lines are horizontal (i.e., m = 0). The distance between the points is
d = ( b 1 m − b 2 m m 2 + 1 ) 2 + ( b 2 − b 1 m 2 + 1 ) 2 , {\displaystyle d={\sqrt {\left({\frac {b_{1}m-b_{2}m}{m^{2}+1}}\right)^{2}+\left({\frac {b_{2}-b_{1}}{m^{2}+1}}\right)^{2}}}\,,}
which reduces to
d = | b 2 − b 1 | m 2 + 1 . {\displaystyle d={\frac {|b_{2}-b_{1}|}{\sqrt {m^{2}+1}}}\,.}
When the lines are given by the general form of the equation of a line (horizontal and vertical lines are included):
a x + b y + c 1 = 0 {\displaystyle ax+by+c_{1}=0\,}
a x + b y + c 2 = 0 , {\displaystyle ax+by+c_{2}=0,\,}
their distance can be expressed as
d = | c 2 − c 1 | a 2 + b 2 . {\displaystyle d={\frac {|c_{2}-c_{1}|}{\sqrt {a^{2}+b^{2}}}}.}
Two lines in three-dimensional space[edit]
Two lines in the same three-dimensional space that do not intersect need not be parallel. Only if they are in a common plane are they called parallel; otherwise they are called skew lines.
Two distinct lines l and m in three-dimensional space are parallel if and only if the distance from a point P on line m to the nearest point on line l is independent of the location of P on line m. This never holds for skew lines.
A line and a plane[edit]
A line m and a plane q in three-dimensional space, the line not lying in that plane, are parallel if and only if they do not intersect.
Equivalently, they are parallel if and only if the distance from a point P on line m to the nearest point in plane q is independent of the location of P on line m.
Two planes[edit]
Similar to the fact that parallel lines must be located in the same plane, parallel planes must be situated in the same three-dimensional space and contain no point in common.
Two distinct planes q and r are parallel if and only if the distance from a point P in plane q to the nearest point in plane r is independent of the location of P in plane q. This will never hold if the two planes are not in the same three-dimensional space.
Extension to non-Euclidean geometry[edit]
This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (May 2017) (Learn how and when to remove this template message)
In non-Euclidean geometry, it is more common to talk about geodesics than (straight) lines. A geodesic is the shortest path between two points in a given geometry. In physics this may be interpreted as the path that a particle follows if no force is applied to it. In non-Euclidean geometry (elliptic or hyperbolic geometry) the three Euclidean properties mentioned above are not equivalent and only the second one,(Line m is in the same plane as line l but does not intersect l ) since it involves no measurements is useful in non-Euclidean geometries. In general geometry the three properties above give three different types of curves, equidistant curves, parallel geodesics and geodesics sharing a common perpendicular, respectively.
Hyperbolic geometry[edit]
See also: hyperbolic geometry
Intersecting, parallel and ultra parallel lines through a with respect to l in the hyperbolic plane. The parallel lines appear to intersect l just off the image. This is just an artifact of the visualisation. On a real hyperbolic plane the lines will get closer to each other and 'meet' in infinity.
While in Euclidean geometry two geodesics can either intersect or be parallel, in hyperbolic geometry, there are three possibilities. Two geodesics belonging to the same plane can either be:
intersecting, if they intersect in a common point in the plane,
parallel, if they do not intersect in the plane, but converge to a common limit point at infinity (ideal point), or
ultra parallel, if they do not have a common limit point at infinity.
In the literature ultra parallel geodesics are often called non-intersecting. Geodesics intersecting at infinity are called limiting parallel.
As in the illustration through a point a not on line l there are two limiting parallel lines, one for each direction ideal point of line l. They separate the lines intersecting line l and those that are ultra parallel to line l.
Ultra parallel lines have single common perpendicular (ultraparallel theorem), and diverge on both sides of this common perpendicular.

Spherical or elliptic geometry[edit]
See also: Spherical geometry and Elliptic geometry
On the sphere there is no such thing as a parallel line. Line a is a great circle, the equivalent of a straight line in spherical geometry. Line c is equidistant to line a but is not a great circle. It is a parallel of latitude. Line b is another geodesic which intersects a in two antipodal points. They share two common perpendiculars (one shown in blue).
In spherical geometry, all geodesics are great circles. Great circles divide the sphere in two equal hemispheres and all great circles intersect each other. Thus, there are no parallel geodesics to a given geodesic, as all geodesics intersect. Equidistant curves on the sphere are called parallels of latitude analogous to the latitude lines on a globe. Parallels of latitude can be generated by the intersection of the sphere with a plane parallel to a plane through the center of the sphere.
Reflexive variant[edit]
If l, m, n are three distinct lines, then l ∥ m ∧ m ∥ n ⟹ l ∥ n . {\displaystyle l\parallel m\ \land \ m\parallel n\ \implies \ l\parallel n.}
In this case, parallelism is a transitive relation. However, in case l = n, the superimposed lines are not considered parallel in Euclidean geometry. The binary relation between parallel lines is evidently a symmetric relation. According to Euclid's tenets, parallelism is not a reflexive relation and thus fails to be an equivalence relation. Nevertheless, in affine geometry a pencil of parallel lines is taken as an equivalence class in the set of lines where parallelism is an equivalence relation.[13][14][15]
To this end, Emil Artin (1957) adopted a definition of parallelism where two lines are parallel if they have all or none of their points in common.[16] Then a line is parallel to itself so that the reflexive and transitive properties belong to this type of parallelism, creating an equivalence relation on the set of lines. In the study of incidence geometry, this variant of parallelism is used in the affine plane.
See also[edit]
Clifford parallel
Limiting parallel
Parallel curve
Ultraparallel theorem
Notes[edit]
Jump up ^ Although this postulate only refers to when lines meet, it is needed to prove the uniqueness of parallel lines in the sense of Playfair's axiom.
Jump up ^ "Mathematical Operators – Unicode Consortium" (PDF). Retrieved 2013-04-21.
Jump up ^ Wylie, Jr. 1964, pp. 92—94
^ Jump up to: a b Heath 1956, pp. 190–194
Jump up ^ Richards 1988, Chap. 4: Euclid and the English Schoolchild. pp. 161–200
Jump up ^ Carroll, Lewis (2009) [1879], Euclid and His Modern Rivals, Barnes & Noble, ISBN 978-1-4351-2348-9
Jump up ^ Wilson 1868
Jump up ^ Einführung in die Grundlagen der Geometrie, I, p. 5
Jump up ^ Heath 1956, p. 194
Jump up ^ Richards 1988, pp. 180–184
Jump up ^ Heath 1956, p. 194
Jump up ^ Only the third is a straightedge and compass construction, the first two are infinitary processes (they require an "infinite number of steps".)
Jump up ^ H. S. M. Coxeter (1961) Introduction to Geometry, p 192, John Wiley & Sons
Jump up ^ Wanda Szmielew (1983) From Affine to Euclidean Geometry, p 17, D. Reidel ISBN 90-277-1243-3
Jump up ^ Andy Liu (2011) "Is parallelism an equivalence relation?", The College Mathematics Journal 42(5):372
Jump up ^ Emil Artin (1957) Geometric Algebra, page 52
References[edit]
Heath, Thomas L. (1956), The Thirteen Books of Euclid's Elements (2nd ed. [Facsimile. Original publication: Cambridge University Press, 1925] ed.), New York: Dover Publications
(3 vols.): ISBN 0-486-60088-2 (vol. 1), ISBN 0-486-60089-0 (vol. 2), ISBN 0-486-60090-4 (vol. 3). Heath's authoritative translation plus extensive historical research and detailed commentary throughout the text.
Richards, Joan L. (1988), Mathematical Visions: The Pursuit of Geometry in Victorian England, Boston: Academic Press, ISBN 0-12-587445-6
Wilson, James Maurice (1868), Elementary Geometry (1st ed.), London: Macmillan and Co.
Wylie, Jr., C.R. (1964), Foundations of Geometry, McGraw–Hill
Further reading[edit]
Papadopoulos, Athanase; Théret, Guillaume (2014), La théorie des parallèles de Johann Heinrich Lambert : Présentation, traduction et commentaires, Paris: Collection Sciences dans l'histoire, Librairie Albert Blanchard, ISBN 978-2-85367-266-5
External links[edit]
Constructing a parallel line through a given point with compass and straightedge
Retrieved from "https://en.wikipedia.org/w/index.php?title=Parallel_(geometry)&oldid=833416177"
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values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Parallel_geometry rootpage-Parallel_geometry skin-vector action-view