2D shapes – Oval/Ellipse

An oval is a 2D shape that is similar to an ellipse. It is a closed, curved shape that is elongated like an egg or an ellipse, but the two ends are rounded instead of pointed. An oval has two axes of symmetry that intersect at its center. The length of the two axes can vary, and an oval can be wider than it is tall or taller than it is wide.

Ovals are commonly found in nature, such as in the shapes of eggs, leaves, and some fruits. They are also used in design and art, as they can create a sense of movement and fluidity in a composition. Ovals are sometimes used as a design element in logos, graphic design, and even in architecture.

There are several formulas that can be used to calculate different properties of an oval 2D shape.

  1. Area of an oval:

The formula to calculate the area of an oval is A = π * a * b, where a and b are the lengths of the major and minor axes respectively. The longer axis is called the major axis, and the shorter axis is called the minor axis.

  1. Perimeter of an oval:

There is no simple formula for the perimeter of an oval. However, an approximate formula can be found using Ramanujan‘s approximation, which gives a reasonably accurate result. The formula is P ≈ π * (3(a + b) – √((3a + b) * (a + 3b))), where a and b are the lengths of the major and minor axes respectively.

  1. Eccentricity of an oval:

The eccentricity of an oval is a measure of how elongated or stretched out it is. It is defined as the ratio of the distance between the foci of the oval to the length of its major axis. The formula to calculate eccentricity is e = c/a, where c is the distance between the foci and a is the length of the major axis.

  1. Semi-major and semi-minor axes of an oval:

The semi-major and semi-minor axes are half the lengths of the major and minor axes respectively. They are denoted by a/2 and b/2. These values can be useful in certain calculations, such as finding the center of the oval.

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