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The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
An array of puzzles and tricks, with a few traps for the unwary 1968 Sep: Counting systems and the relationship between numbers and the real world 1968 Oct: MacMahon's color triangles and the joys of fitting them together 1968 Nov: On the ancient lore of dice and the odds against making a point 1968 Dec
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen or retracing any lines.
The states of an n-disk puzzle, and the allowable moves from one state to another, form an undirected graph, the Hanoi graph, that can be represented geometrically as the intersection graph of the set of triangles remaining after the n th step in the construction of the Sierpiński triangle.
Some types of dissection puzzle are intended to create a large number of different geometric shapes. The tangram is a popular dissection puzzle of this type. The seven pieces can be configured into one of a few home shapes, such as the large square and rectangle that the pieces are often stored in, to any number of smaller squares, triangles, parallelograms, or esoteric shapes and figures.
Dudeney's hinged dissection of a triangle into a square. Animation of hinged dissection from hexagram to triangle to square. The concept of hinged dissections was popularised by the author of mathematical puzzles, Henry Dudeney. He introduced the famous hinged dissection of a square into a triangle (pictured) in his 1907 book The Canterbury ...
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