Triangles, quadrilaterals and polygons
... There is an obvious pattern here – any polygon with n sides can be split into n-2 triangles. Since the interior angle sum of a triangle is 180°, the sum of the interior angles of a polygon can be given by the formula Angle sum = 180(n -2)° where n is the number of the sides in the polygon. Example ( ...
... There is an obvious pattern here – any polygon with n sides can be split into n-2 triangles. Since the interior angle sum of a triangle is 180°, the sum of the interior angles of a polygon can be given by the formula Angle sum = 180(n -2)° where n is the number of the sides in the polygon. Example ( ...
Classifying Polygons
... pentagon inside of the building that houses an outdoor courtyard. Looking at the picture, the building is divided up into 10 smaller sections. What are the shapes of these sections? Are any of these division lines diagonals? How do you know? ...
... pentagon inside of the building that houses an outdoor courtyard. Looking at the picture, the building is divided up into 10 smaller sections. What are the shapes of these sections? Are any of these division lines diagonals? How do you know? ...
Lesson 1.5 • Triangles and Special Quadrilaterals
... relationships among their sides. Measure the lengths of the three sides of ABC. If none of the side lengths are equal, the triangle is a scalene triangle. If two or more of the sides are equal in length, the triangle is isosceles. If all three sides are equal in length, it is equilateral. Because ...
... relationships among their sides. Measure the lengths of the three sides of ABC. If none of the side lengths are equal, the triangle is a scalene triangle. If two or more of the sides are equal in length, the triangle is isosceles. If all three sides are equal in length, it is equilateral. Because ...
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.