7.3 Proving Triangles Similar
... Finding the Length of Similar Triangles • Before rock climbing, Darius wants to know how high he will climb. He places a mirror on the ground and walks backward until he can see the top of the cliff in the mirror. What is the height of the cliff? ...
... Finding the Length of Similar Triangles • Before rock climbing, Darius wants to know how high he will climb. He places a mirror on the ground and walks backward until he can see the top of the cliff in the mirror. What is the height of the cliff? ...
Similar Triangles and the Pythagorean Theorem
... Two triangles are similar if they contain angles of the same measure. Similar triangles have the same shape but may be different in size. Also, the ratios of corresponding side lengths of the triangles are equal. SIMILAR TRIANGLE FACTS If two triangles have three angles of the same measure, the tria ...
... Two triangles are similar if they contain angles of the same measure. Similar triangles have the same shape but may be different in size. Also, the ratios of corresponding side lengths of the triangles are equal. SIMILAR TRIANGLE FACTS If two triangles have three angles of the same measure, the tria ...
MA.912.G.4.5 Apply theorems involving segments divided
... There is a lot of situations where similar triangles naturally arise ...
... There is a lot of situations where similar triangles naturally arise ...
My Favourite Problem No.5 Solution
... Note: You may think that this only gives the answer for equilateral triangles and might not work for other triangles. There is a clever rule involving affine transformations , such as stretches, translation, reflection etc., that allows us to generalise from this result. Affine transformations of sh ...
... Note: You may think that this only gives the answer for equilateral triangles and might not work for other triangles. There is a clever rule involving affine transformations , such as stretches, translation, reflection etc., that allows us to generalise from this result. Affine transformations of sh ...
Penrose tiling
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A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right. A Penrose tiling has many remarkable properties, most notably:It is non-periodic, which means that it lacks any translational symmetry. It is self-similar, so the same patterns occur at larger and larger scales. Thus, the tiling can be obtained through ""inflation"" (or ""deflation"") and any finite patch from the tiling occurs infinitely many times.It is a quasicrystal: implemented as a physical structure a Penrose tiling will produce Bragg diffraction and its diffractogram reveals both the fivefold symmetry and the underlying long range order.Various methods to construct Penrose tilings have been discovered, including matching rules, substitutions or subdivision rules, cut and project schemes and coverings.