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The respective lengths a, b, and c of the sides of these three polygons satisfy the equation a 2 + b 2 = c 2, so line segments with these lengths form a right triangle (by the converse of the Pythagorean theorem). The ratio of the side length of the hexagon to the decagon is the golden ratio, so this triangle forms half of a golden rectangle. [8]
A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a ...
The base cases of the induction are the 0-ball and the 1-ball, which can be checked directly using the facts Γ(1) = 1 and Γ( 3 / 2 ) = 1 / 2 · Γ( 1 / 2 ) = √ π / 2 . The inductive step is similar to the above, but instead of applying proportionality to the volumes of the (n − 2)-balls, the inductive ...
On the Sphere and Cylinder (Greek: Περὶ σφαίρας καὶ κυλίνδρου) is a treatise that was published by Archimedes in two volumes c. 225 BCE. [1] It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so. [2]
Modern-day Spaldeen. A Spalding Hi-Bounce Ball, often called a Spaldeen or a Pensie Pinkie, is a rubber ball, described as a tennis ball core without the felt. [1] These balls are commonly used in street games developed in the mid-20th century, such as Chinese handball (a variation on American handball), Australian Handball, stoop ball, hit-the-penny (involving trying to make a penny flip on a ...
The centimetre (SI symbol: cm) is a unit of length in the metric system equal to 10 −2 metres ( 1 / 100 m = 0.01 m). To help compare different orders of magnitude , this section lists lengths between 10 −2 m and 10 −1 m (1 cm and 1 dm).
[2] [3] Another equivalent way to define the width of a compact curve or of a convex set is by looking at its orthogonal projection onto a line. In both cases, the projection is a line segment, whose length equals the distance between support lines that are perpendicular to the line. So, a curve or a convex set has constant width when all of ...
Regulation size and weight for a football is a circumference of 68–70 cm (27–28 in) and a weight of 410–450 g (14–16 oz). The ball is inflated to a pressure of 0.6–1.1 bars (8.7–16.0 psi) at sea level. [20] This is known as "Size 5". Smaller balls, Sizes 1, 3, and 4, are also produced for younger players or as training tools. [20]