Module 5 Class Notes
... four cases given above are all the ways to give three independent scalars for a triangle (e.g. AAS and SAA are the same as ASA since you can find the third angle, and SSA is the same as ASS by reordering). ...
... four cases given above are all the ways to give three independent scalars for a triangle (e.g. AAS and SAA are the same as ASA since you can find the third angle, and SSA is the same as ASS by reordering). ...
Lesson 5.3 File
... consecutive sides. You can make a kite by constructing two different isosceles triangles on opposite sides of a common base and then removing the base. In an isosceles triangle, the angle between the two congruent sides is called the __________ angle. For this reason, we’ll call angles between the p ...
... consecutive sides. You can make a kite by constructing two different isosceles triangles on opposite sides of a common base and then removing the base. In an isosceles triangle, the angle between the two congruent sides is called the __________ angle. For this reason, we’ll call angles between the p ...
Document
... you can rule out the AAA combination by finding a counterexample for the following conjecture: Conjecture: If the three angles of one triangle are congruent to the three angles of another triangle, then the triangles are congruent. Counterexample: In the triangles below there are three pairs of cong ...
... you can rule out the AAA combination by finding a counterexample for the following conjecture: Conjecture: If the three angles of one triangle are congruent to the three angles of another triangle, then the triangles are congruent. Counterexample: In the triangles below there are three pairs of cong ...
Penrose tiling
.svg?width=300)
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.