flammable
发表于 2025-3-23 10:48:56
https://doi.org/10.1007/978-3-662-00516-3. In all solutions the triangle . is oriented counterclockwise. The first solution uses . and can be followed on Fig. 12.1. Let .., .., and .. be the centers of the equilateral triangles ..., ..., and ..., respectively.
tinnitus
发表于 2025-3-23 17:00:16
IsometriesOur discussion begins with those transformations that lie at the heart of the notion of equality in geometry. We tend to identify two geometric figures and call them . (or . when we are very rigorous) if we can place one on top of the other to coincide exactly.
Fracture
发表于 2025-3-23 20:05:41
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optic-nerve
发表于 2025-3-24 01:05:52
IsometriesWhat is the composition of two reflections? Where does it map the first triangle?
Hemiplegia
发表于 2025-3-24 05:41:25
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anagen
发表于 2025-3-24 08:23:17
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Opponent
发表于 2025-3-24 14:26:37
IsometriesThe composition of the two reflections is either a translation or a rotation, and this transformation maps the triangle . to itself. It cannot be a translation because its repeated applications would move the triangle away from itself. Therefore, it is a rotation. The triangle that is invariant under some rotation is the equilateral triangle.
incarcerate
发表于 2025-3-24 16:10:39
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吸引人的花招
发表于 2025-3-24 20:37:25
InversionsPlacing the center of inversion at the origin of the coordinate system, the inversions have the equations . and ., so their composition has the equation ., which is the homothety of center . and radius ..
小卷发
发表于 2025-3-25 00:05:55
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