Editing Tangram (section)

==Paradoxes==
[[File:tangram_paradox_explanation.svg|thumb|Explanation of the two-monks paradox:<br />In figure 1, side lengths are labelled assuming the square has unit sides.<br />In figure 2, overlaying the bodies shows that footless body is larger by the foot's area. The change in area is often unnoticed as √2 is close to 1.5.]]
A tangram [[paradox]] is a dissection fallacy: Two figures composed with the same set of pieces, one of which seems to be a proper subset of the other.<ref name="mathematica">[http://mathworld.wolfram.com/TangramParadox.html Tangram Paradox], by Barile, Margherita, From MathWorld – A Wolfram Web Resource, created by Eric W. Weisstein.</ref> One famous paradox is that of the two [[monk]]s, attributed to [[Henry Dudeney]], which consists of two similar shapes, one with and the other missing a foot.<ref name="dudeney">{{cite book |author=Dudeney, H. |title=Amusements in Mathematics |publisher=Dover Publications |location=New York |year=1958}}</ref> In reality, the area of the foot is compensated for in the second figure by a subtly larger body.

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The two-monks paradox&nbsp;– two similar shapes but one missing a foot:
[[File:Two monks tangram paradox.svg|thumb|left]]
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The Magic Dice Cup tangram paradox&nbsp;– from [[Sam Loyd]]'s book ''The 8th Book of Tan'' (1903).<ref name="eighth book 1"/> Each of these cups was composed using the same seven geometric shapes. But the first cup is whole, and the others contain vacancies of different sizes. (Notice that the one on the left is slightly shorter than the other two. The one in the middle is ever-so-slightly wider than the one on the right, and the one on the left is narrower still.)<ref>{{cite web|title=The Magic Dice Cup|date=2 April 2011 |url=https://www.futilitycloset.com/2011/04/02/the-magic-dice-cup/}}</ref>
[[File:The Magic Dice Cup tangram paradox.svg|thumb|left]]
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Clipped square tangram paradox&nbsp;– from Loyd's book ''The Eighth Book of Tan'' (1903):<ref name="eighth book 1">{{cite book |url=http://www.tangram-channel.com/the-eighth-book-of-tan-by-sam-loyd-page-1/ |title=The 8th Book of Tan by Sam Loyd |year=1903 |via=Tangram Channel}}</ref>

{{blockquote|The seventh and eighth figures represent the mysterious square, built with seven pieces: then with a corner clipped off, and still the same seven pieces employed.<ref name="loyd">{{cite book |author=Loyd, Sam |title=The eighth book of Tan – 700 Tangrams by Sam Loyd with an introduction and solutions by Peter Van Note |publisher=Dover Publications |location=New York |year= 1968|page=25 }}</ref>}}
[[File:squares.GIF|thumb|left]]
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