Editing Missing square puzzle (section)

==Similar puzzles==
[[File:Missing square edit.gif|thumb|left|150px|A variant of Mitsunobu Matsuyama's "paradox"]]
[[File:Loyd64-65-dis b.svg|thumb|right|200px|[[Sam Loyd]]'s paradoxical dissection]]
[[Sam Loyd]]'s [[chessboard paradox]] demonstrates two rearrangements of an 8×8 square. In the "larger" rearrangement (the 5×13 rectangle in the image to the right), the gaps between the figures have a combined unit square more area than their square gaps counterparts, creating an illusion that the figures there take up more space than those in the original square figure.<ref>{{Cite news|url=https://mathblag.wordpress.com/2011/08/28/a-paradoxical-dissection/|title=A Paradoxical Dissection|date=2011-08-28|work=mathblag|access-date=2018-04-19|language=en-US}}</ref> In the "smaller" rearrangement (the shape below the 5×13 rectangle), each quadrilateral needs to overlap the triangle by an area of half a unit for its top/bottom edge to align with a grid line, resulting overall loss in one unit square area.

Mitsunobu Matsuyama's paradox uses four congruent [[quadrilateral]]s and a small square, which form a larger square. When the quadrilaterals are rotated about their centers they fill the space of the small square, although the total area of the figure seems unchanged. The apparent paradox is explained by the fact that the side of the new large square is a little smaller than the original one. If ''θ'' is the angle between two opposing sides in each quadrilateral, then the ratio of the two areas is given by [[Secant (trigonometry)|sec<sup>2</sup>&nbsp;''θ'']]. For ''θ'' = 5°, this is approximately 1.00765, which corresponds to a difference of about 0.8%.

[[File:the_disappearing_bicyclist_vanishing_puzzle.svg|thumb|upright|link={{filepath:the_disappearing_bicyclist_vanishing_puzzle.svg}}|Interactive SVG of ''The Disappearing Bicyclist'' &ndash; in [{{filepath:the_disappearing_bicyclist_vanishing_puzzle.svg}} the SVG file,] move the pointer to rotate the disc]]
A [[vanishing puzzle]] is a mechanical optical illusion showing different numbers of a certain object when parts of the puzzle are moved around.<ref>The Guardian, [http://www.theguardian.com/science/alexs-adventures-in-numberland/gallery/2014/apr/01/vanishing-leprechaun-disappearing-dwarf-puzzles-pictures ''Vanishing Leprechaun, Disappearing Dwarf and Swinging Sixties Pin-up Girls – puzzles in pictures'']</ref>