The kites are the quadrilaterals that have an axis of symmetry along one of their diagonals. Exactly one pair of opposite angles are bisected by a diagonal.One diagonal is a line of symmetry (it divides the quadrilateral into two congruent triangles).(In the concave case it is the extension of one of the diagonals.) One diagonal is the perpendicular bisector of the other diagonal.Two pairs of adjacent sides are equal (by definition).CharacterizationsĪ quadrilateral is a kite if and only if any one of the following statements is true: The tiling that it produces by its reflections is the deltoidal trihexagonal tiling. There are only eight polygons that can tile the plane in such a way that reflecting any tile across any one of its edges produces another tile one of them is a right kite, with 60°, 90°, and 120° angles. That is, for these kites the two equal angles on opposite sides of the symmetry axis are each 90 degrees. the kites that can be inscribed in a circle) are exactly the ones formed from two congruent right triangles. The kites that are also cyclic quadrilaterals (i.e. On the other hand, “diamond” works just fine.An equidiagonal kite that maximizes the ratio of perimeter to diameter, inscribed in a Reuleaux triangleĪmong all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite with angles π/3, 5π/12, 5π/6, 5π/12. Perhaps we should say “and now the players are about to take their positions on the kite.” It may be very close to a square, but square it is not. This is the exact shape that home plate and the bases form. In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal length sides that are adjacent to each other. Therefore, if Cannon seeks mathematical precision, the correct term for a baseball field, as represented by home plate and the bases on the field, is a kite. The reason for this is that the center of second base is placed at the exact 90-foot intersection. As a result, half of the width of the base, or 7 1 / 2 inches (a standard base is 15 inches wide), is actually outside of the 90-foot square. The distance from the apex of the pentagon (the pointy part) to the back of first base (closest to right field) is 90 feet. Similarly, the distance from the apex of home plate to the back of third base is 90 feet. However, the distance from the side of first base on the foul line, to the back of second base (facing left field) is 90 feet, 7 1 / 2 inches - the same as the distance from the foul line side of third base to the opposite, back side of second base (facing right field). The reason is that the physical representation of the infield - namely home plate, the two foul lines and the three bases, do not form an exact square. But beyond that, a baseball diamond or baseball square, if you prefer, is not, in fact, a square. George Carlin would have agreed that baseball is a sport of imprecision and subjectivity. I doubt that those who first coined the term “ baseball diamond” had much interest in mathematical precision. In his example, he states that a baseball “diamond” is not a diamond, but a square and that it should be referred to as such. I read James Cannon’s May 26 Free for All letter in which he asks that proper math terms be used to describe a shape.
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