"Britney Gallivan Britney Crystal Gallivan (born 1985) of Pomona, California, is best known for determining the maximum number of times that paper or other materials can be folded in half. In January 2002, while a junior in high school, Gallivan demonstrated that a single piece of toilet paper 4000 ft (1200 m) in length can be folded in half twelve times. This was contrary to the popular conception that the maximum number of times any piece of paper could be folded in half was seven. She calculated that, instead of folding in half every other direction, the least volume of"
"desired number of folds to be carried out in alternate directions. For paper that is not square, e.g., having a 2:1 ratio, the above equation still gives an accurate limit. Gallivan's story was mentioned in the episode ""Identity Crisis"" of ""Numb3rs"", she served as a consultant and was mentioned in an episode of ""MythBusters"" on the Discovery Channel in 2007, and in episode 3 of ""QI""'s F series. Britney Gallivan Britney Crystal Gallivan (born 1985) of Pomona, California, is best known for determining the maximum number of times that paper or other materials can be folded in half. In January"
"to form developable surfaces that are not flat. Wet-folding origami allows an even greater range of shapes. The maximum number of times an incompressible material can be folded has been derived. With each fold a certain amount of paper is lost to potential folding. The loss function for folding paper in half in a single direction was given to be formula_4, where ""L"" is the minimum length of the paper (or other material), ""t"" is the material's thickness, and ""n"" is the number of folds possible. The distances ""L"" and ""t"" must be expressed in the same units, such as"
"The paper size is 'double folio', with two pages printed on each side (four pages per sheet). After printing the paper was folded once to the size of a single page. Typically, five of these folded sheets (10 leaves, or 20 printed pages) were combined to a single physical section, called a quinternion, that could then be bound into a book. Some sections, however, had as few as four leaves or as many as 12 leaves. Some sections may have been printed in a larger number, especially those printed later in the publishing process, and sold unbound. The pages were"
"size exactly formula_1 m × formula_2 m. Rounded to the nearest millimetre, that is . Successive paper sizes in the series A1, A2, A3, and so forth, are defined by halving the preceding paper size across the larger dimension. This also effectively halves the area of each sheet. The most frequently used paper size is A4 measuring . The significant advantage of this system is its scaling: if a sheet with an aspect ratio of is divided into two equal halves parallel to its shortest sides, then the halves will again have an aspect ratio of . Folded brochures of"
"paper is fed horizontally over 2 unpowered rollers until it hits a paper stop, at which point a dull blade pushes down on the paper and in between the 2 rollers to create the fold. Although the knife folder is slower than buckle folders, it is more precise and can handle extreme grammages very well. It also has small folding tolerances, but is a more complex machine. Folding a paper more than once in the same direction (i.e. with parallel creases) is called parallel folding. Common examples of this are the half fold, letter fold, gate fold, and Z-fold. A"
"the sheet of paper is folded in half widthwise, let ""c"" be the length of the new short side: ""c"" = . If we take the ratio of the newly folded paper we have: formula_3 Therefore, the aspect ratio is preserved for the new dimensions of the folded paper. Weights are easy to calculate as well: a standard A4 sheet made from 80 g/m paper weighs 5 g (as it is of an A0 page, measuring 1 m), allowing one to easily compute the weight—and associated postage rate—by counting the number of sheets used. The advantages of basing a paper"
"once to form two leaves or four pages, are referred to as ""folios"" (from Latin, ""foliō"", ablative of ""folium"", leaf). Those made by printing four text pages on each side of a sheet of paper and folding the paper twice to form a gathering containing four leaves or eight pages are called ""quartos"" (fourths). Similarly, books made by printing eight pages of text on each side of a sheet, which was then folded three times to form gatherings of eight leaves or sixteen pages each, are called ""octavos"". The size of the resulting pages in these cases depends, of course,"
"inches. This result was derived by Gallivan in 2001, who also folded a sheet of paper in half 12 times, contrary to the popular belief that paper of any size could be folded at most eight times. She also derived the equation for folding in alternate directions. The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete cut. The solution, known as the fold-and-cut theorem, states that any shape with straight sides can be obtained. A practical problem is how to fold a map so that it may"
"(the ones that fold in to the middle) are usually 1/32"" to 1/8"" smaller than the inner panels (the ones covered by the panels that fold in) to allow for proper folding and nesting. Takes a concertina fold, folded in half down the middle to create 8 individual sections. Also known as cross fold and quarter fold. Folded leaflet Leaflets that are folded are usually used for advertising or marketing purposes, or for information supplementary to labels. There are many types of folds; only the most popular types are listed here. Although it is difficult to put a date on"
"cm) tall, and as such does not necessarily indicate the actual printing format of the books, which may even be unknown as is the case for many modern books. These terms are discussed in greater detail in Book sizes. A quarto (from Latin ""quartō"", ablative form of ""quartus"", fourth ) is a book or pamphlet made up of one or more full sheets of paper on which 8 pages of text were printed, which were then folded two times to produce four leaves. Each leaf of a quarto book thus represents one fourth the size of the original sheet. Each"
"employs a folding angle of about 135° on each side (that is, a complete oscillation of about 2 × 270° for each complete double fold). Strictly speaking, the first double fold is more than one complete oscillation since the flap needs to be folded from vertical to its starting position before the counting begins. The process was analyzed and criticized by Nicholson Baker in his 2001 book ""Double Fold: Libraries and the Assault on Paper"". Double fold A double fold is a process of folding a paper sample first backwards and then forwards about the same line, i.e. one complete"
"their actual size is rather different. A folio (from Latin foliō, abl. of folium, leaf ) is a book or pamphlet made up of one or more full sheets of paper, on each sheet of which four pages of text are printed, two on each side; each sheet is then folded one time to produce two leaves. Each leaf of a folio book thus is one half the size of the original sheet. This contrasts with a quarto, folding each sheet twice, and octavo, folding each sheet three times. Unlike the folio, these last, and further types involving more folds,"
"halved Letter size, , meets the needs of many applications. It is variably known as ""Statement"", ""Stationery"", ""Memo"", ""Half Letter"", ""Half A"" (from ANSI sizes) or simply ""Half Size"". Like the similar-sized ISO A5, it is used for everything from personal letter writing to official aeronautical maps. Organizers, notepads, and diaries also often use this size of paper; thus 3-ring binders are also available in this size. Booklets of this size are created using word processing tools with landscape printing in two columns on letter paper which are then cut or folded into the final size. In 1996, the American"
"Octavo Octavo, a Latin word meaning ""in eighth"" or ""for the eighth time"", (abbreviated 8vo, 8°, or In-8) is a technical term describing the format of a book, which refers to the size of leaves produced from folding a full sheet of paper on which multiple pages of text were printed to form the individual sections (or ""gatherings"") of a book. An octavo is a book or pamphlet made up of one or more full sheets of (e.g. A2 paper) on which 16 pages of text were printed, which were then folded three times to produce eight leaves. Each leaf"
"the same sheet or piggybacking a project on a vacant, unused portion of a print sheet. Sheet-fed presses are generally ""full sheet"" (28"" x 40""), ""half sheet"" (28"" x 19""), or ""quarter sheet"" (13"" x 19""). In offset printing, the first sheet costs more than the next 1,000. Gang-run printing allows multiple jobs to share the setup cost. For example, a 28"" x 40"" sheet can hold 9 4"" x 6"" at 5,000 or 18 2,500 postcards (each card takes 4.25"" x 6.25"" on the sheet to accommodate full bleed. Gang-run printing has been one of the driving forces in"
"follow the same ratio principle as the A series pages. For example, if an A4 page is folded in half so that it is A5 in size, it will fit into a C5 envelope (which will be the same size as a C4 envelope folded in half). The lengths of ISO C series paper are therefore ≈ 1.09 times those of A-series paper. A, B, and C paper fit together as part of a geometric progression, with ratio of successive side lengths of , though there is no size half-way between B""n"" and A(""n"" − 1): A4, C4, B4, ""D4"","
"form of ""quartus"", fourth) historically was a book printed on a sheet of paper folded twice to produce four leaves (or eight pages), each leaf one fourth the size of the original sheet printed. Because the actual format of many modern books cannot be determined from examination of the books, bibliographers may not use these terms in scholarly descriptions. In the hand press period (up to about 1820) books were manufactured by printing text on both sides of a full sheet of paper and then folding the paper one or more times into a group of leaves or ""gathering"". The"
"printing, the format of the book or pamphlet depended on the size of the paper used and the number of times it was folded. If a page was only folded once, it was called a folio. If it was folded twice, it was known as a quarto. An octave was a paper folded three times. A pamphlet was usually 1-12 sheets of paper folded in quarto, or 8-96 pages. It was sold for one or two pennies apiece. The printing of a pamphlet involved many people: the author, the printer, suppliers, print-makers, compositor, correctors, pressmen, binders, and distributors. Once the"
"of the aspect ratio. In each series of sizes (for example, series A), the largest size is numbered 0 (for example, A0), and each successive size (for example, A1, A2, etc.) has half the area of the preceding sheet and can be cut by halving the length of the preceding size sheet. The new measurement is rounded down to the nearest millimetre. A folded brochure can be made by using a sheet of the next larger size (for example, an A4 sheet is folded in half to make a brochure with size A5 pages. An office photocopier or printer can"
"Also known as a spiral fold, tri fold, brochure fold, business letter, C fold, roll fold and barrel fold. Also known as a window fold. In double parallel folds the paper is folded in half and then folded in half again with a fold parallel to the first fold. To allow for proper nesting the two inside folded panels are 1/32"" to 1/8"" smaller than the two outer panels. In double gatefolds there are three parallel folds. The left and right edges of the paper fold and meet in the middle, without overlapping, along a center fold. The outer panels"
"any size can be made by using sheets of the next larger size, e.g. A4 sheets are folded to make A5 brochures. The system allows scaling without compromising the aspect ratio from one size to another—as provided by office photocopiers, e.g. enlarging A4 to A3 or reducing A3 to A4. Similarly, two sheets of A4 can be scaled down and fit exactly on 1 sheet without any cutoff or margins. The behavior of the aspect ratio is easily proven: on a sheet of paper, let ""a"" be the long side and ""b"" be the short side; thus, = . When"
"Foolscap folio Foolscap folio (commonly contracted to foolscap or folio and in short FC) is paper cut to the size of (for ""normal"" writing paper, ). This was a traditional paper size used in Europe and the British Commonwealth, before the adoption of the international standard A4 paper. A full foolscap paper sheet is actually in size, and a folio sheet of any type is half the standard sheet size or a subdivision of this into halves, quarters and so on. Ring binders or lever arch files designed to hold foolscap folios are often used to hold A4 paper ()."
"not sharp enough to cut through the paper and simply strikes and creases the paper along the line where the fold is required. Ideally, knife folding is used with thick paper, for ""cross folds"" (commonly employed for maps and also known as a ""French fold"") or if the paper has been stitched during the folding process; stitched sheets can ruin high friction rollers. Folding machines exclusively used for folding paper are commonly referred to as paper folders. These machines are typically used for creating letter folds (C Folds) and accordion folds (Z Folds). Other commonly used folds include a half"
"delivery from a mill to a specific pressroom can also depend on the press room ability to accept enough trucks or rail cars. A newspaper roll's width is called its web width and is defined by how many front pages it can print. A full roll prints four front pages with four back pages behind it (two front and back on each of the two sections). Modern printing facilities most efficiently print newspapers in multiples of eight pages on a full newsprint roll in two sections of four pages each. The two sections are then cut in half. Faced with"
"ten, the third of ten, and the fourth of six. Although the book is of the size called quarto, the method of printing must have been page by page, so it is doubtful that each sheet was folded twice in the usual quarto manner, but more probable that it was printed four pages to a sheet of paper approximately 9⅛ by 14 inches, which was folded once. The volume was printed using the xylographic technique, printing each page of text from one hand carved woodblock. Vertical lines long the inner margins of some pages were made by the inked edge"
"texts were beyond the typesetters' capacity to correct. The Folio was typeset and bound in ""sixes"" – 3 sheets of paper, taken together, were folded into a booklet-like quire or gathering of 6 leaves, 12 pages. Once printed, the ""sixes"" were assembled and bound together to make the book. The sheets were printed in 2-page formes, meaning that pages 1 and 12 of the first quire were printed simultaneously on one side of one sheet of paper (which became the ""outer"" side); then pages 2 and 11 were printed on the other side of the same sheet (the ""inner"" side)."
"Double fold A double fold is a process of folding a paper sample first backwards and then forwards about the same line, i.e. one complete oscillation. The number of double folds that is required to make a test piece break is used to determine the material's folding endurance and fold number. The total folding angle (about the folding line) differs depending on which folding tester is used, for instance the Köhler–Molin instrument folds about 156° on each side of the vertical line, resulting in a complete oscillation of about 2 × 312° for each double fold, while the MIT instrument"
"cross fold is when a paper is folded once, then rotated 90 degrees and folded again. The creases therefore cross each other at right angles. The most basic cross fold is the French fold, or right-angle fold. Other examples include the 16-page broadside and the 12-page letter. Book folding Book folding is the stage of the book production process in which the pages of the book are folded after printing and before binding. Until the middle of the 19th century, book folding was done by hand, and was a trade. In the 1880s and 1890s, book folding machines by Brown"
"in quarto editions. Christopher Marlowe's ""Doctor Faustus"", for example, was published as a quarto in 1604 (Q1), with a second quarto edition in 1609. The same is true of poems, Shakespeare's poem ""Venus and Adonis"" being first printed as a quarto in 1593 (Q1), with a second quarto edition (Q2) in 1594. In Spanish culture, a similar concept of separate editions of plays is known as ""comedia suelta"". Quarto Quarto (abbreviated Qto, 4to or 4°) is a book or pamphlet produced from full ""blanksheets"", each of which is printed with eight pages of text, four to a side, then folded"
"non-standard F4 paper size is common in Southeast Asia. It is a transitional size with the shorter side from ISO A4 (210 mm) and the longer side from British Foolscap (13 in, 330 mm) and is sometimes known as ""(metric) foolscap"" or ""folio"" as well. In Indonesia and Philippines, F4 paper is 215 × 330 mm (8.5 × 13 in). In Indonesia it is sometimes called Folio, while in Philippines it is sometimes also called Long Bond. A sheet of F4 can be cut from a sheet of SRA4 with very little wastage. The size is also smaller than its"
"Quarto Quarto (abbreviated Qto, 4to or 4°) is a book or pamphlet produced from full ""blanksheets"", each of which is printed with eight pages of text, four to a side, then folded twice to produce four leaves (that is, eight book pages). Each printed page presents as one-fourth size of the full blanksheet. The earliest known European printed book is a quarto, the ""Sibyllenbuch"", believed to have been printed by Gutenberg in 1452–53, before the ""Gutenberg Bible"", surviving only as a fragment. Quarto is also used as a general description of size of books that are about 12 inches (30"
"the page. To prepare documents for comb binding there are special 19-hole punches for letter paper and 23-hole punches for A4 paper. The holes are usually rectangular in shape, to accommodate the plastic binding combs. Specialized punches are also used for the similar but incompatible coil binding process. There are office models available for the perforation of 1 to 150 sheets of paper, and industrial models for up to 470 sheets. Most multiple-hole and many single-hole punches accumulate the waste paper circles (chads) in a chamber, which must be periodically emptied in order to allow the continued operation of the"