Lemon (geometry) in the context of "Ball (gridiron football)"

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⭐ Core Definition: Lemon (geometry)

In geometry, a lemon is a geometric shape that is constructed as the surface of revolution of a circular arc of angle less than half of a full circle rotated about an axis passing through the endpoints of the lens (or arc). The surface of revolution of the complementary arc of the same circle, through the same axis, is called an apple.

The apple and lemon together make up a spindle torus (or self-crossing torus or self-intersecting torus). The lemon forms the boundary of a convex set, while its surrounding apple is non-convex.

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👉 Lemon (geometry) in the context of Ball (gridiron football)

In Northern America, a football (also called a pigskin) is a ball, roughly in the form of a lemon, used in the context of playing gridiron football. Footballs are often made of cowhide leather, as such a material is required in professional and collegiate football, although footballs used in recreation and organized youth leagues may be made of rubber, plastic or composite leather (high school football rule books still allow inexpensive all-rubber footballs, though they are less common than leather).

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Lemon (geometry) in the context of Torus

In geometry, a torus (pl.: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut.

If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus (or self-crossing torus or self-intersecting torus). If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a toroid, as in a square toroid.

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Lemon (geometry) in the context of Vesica piscis

The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other. In Latin, "vesica piscis" literally means "bladder of a fish", reflecting the shape's resemblance to the conjoined dual air bladders (swim bladder) found in most fish. In Italian, the shape's name is mandorla ("almond"). A similar shape in three dimensions is the lemon.

This figure appears in the first proposition of Euclid's Elements, where it forms the first step in constructing an equilateral triangle using a compass and straightedge. The triangle has as its vertices the two disk centers and one of the two sharp corners of the vesica piscis.

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LINKED FROM (PARENTS)
← Torus ← Ball (gridiron football) ← Ring torus ← Vesica piscis
LINKS TO (CHILDREN)
Geometry → Geometric shape → Surface of revolution → Circular arc → Angle → Torus → Vesica piscis → Torus → Convex set →