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The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...
A twist-hinge dissection is one which use a three-dimensional "hinge" which is placed on the edges of pieces rather than their vertices, allowing them to be "flipped" three-dimensionally. [ 10 ] [ 11 ] As of 2002, the question of whether any two polygons must have a common twist-hinged dissection remains unsolved.
For example, the sum of the three angles α + β + γ depends on the size of the triangle. In addition, similar triangles cannot be unequal, so the problem of constructing a triangle with specified three angles has a unique solution.
The theorem of Theon of Smyrna states that the sum of two consecutive triangle numbers is a square. [ 3 ] His On Mathematics Useful for the Understanding of Plato is not a commentary on Plato's writings but rather a general handbook for a student of mathematics.
The other interior angle (at the North Pole) can be made larger than 90°, further emphasizing the failure of this statement. However, since the Euclid's exterior angle theorem is a theorem in absolute geometry it is automatically valid in hyperbolic geometry.
An example spangram with corresponding theme words: PEAR, FRUIT, BANANA, APPLE, etc. ... NYT Strands Spangram Answer Today. Today's spangram answer on Sunday, December 15, 2024, is LUNARPHASE. ...
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