Review for Quizzes and Tests
... Lengths of sides that make a triangle Type of triangle – acute, obtuse, right Largest Side across from largest angle Exterior angle = sum of two remote interior angles Short cuts to prove triangles congruent and Congruency statement Problems will be similar to what you have done for homework problem ...
... Lengths of sides that make a triangle Type of triangle – acute, obtuse, right Largest Side across from largest angle Exterior angle = sum of two remote interior angles Short cuts to prove triangles congruent and Congruency statement Problems will be similar to what you have done for homework problem ...
Tiling the pentagon
... giving a tiling with n + 5 pentagons. This process can be repeated so as to give tilings for all n¿6. This procedure will not produce edge-to-edge tilings for n¿11. However, we can prove that edge-to-edge tilings are possible. Theorem 1. A pentagon P can always be dissected into n pentagons which fo ...
... giving a tiling with n + 5 pentagons. This process can be repeated so as to give tilings for all n¿6. This procedure will not produce edge-to-edge tilings for n¿11. However, we can prove that edge-to-edge tilings are possible. Theorem 1. A pentagon P can always be dissected into n pentagons which fo ...
Important things to remember for the Geometry EOC
... b. Rotational symmetry (angle of rotation where figure repeats) c. Point symmetry (figure repeats every 180º) 9. Tessellations: Repeated tile pattern, no gaps or overlaps 10.Angles Pairs a. Complementary (add up to 90) b. Supplementary (add up to 180) c. Vertical (are congruent) d. Linear pair (are ...
... b. Rotational symmetry (angle of rotation where figure repeats) c. Point symmetry (figure repeats every 180º) 9. Tessellations: Repeated tile pattern, no gaps or overlaps 10.Angles Pairs a. Complementary (add up to 90) b. Supplementary (add up to 180) c. Vertical (are congruent) d. Linear pair (are ...
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.