## What is Ptolemy's theorem used for?

## What is the triangle inequality theorem in geometry?

triangle inequality, in Euclidean geometry, theorem that **the sum of any two sides of a triangle is greater than or equal to the third side**; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

## When was Ptolemy's theorem discovered?

Every right triangle (in fact every triangle) can be circumscribed by a circle. **Six centuries** later, Greek mathematician Claudius Ptolemy (ca. 90–ca. 168 CE) discovered a relationship between the side lengths and the diagonals of any quadrilateral inscribed in a circle.

## What is Ptolemy's geocentric model?

Ptolemy placed the Earth at the centre of his geocentric model. ... He believed that **the Moon was orbiting on a sphere closest to the Earth**, followed by Mercury, then Venus and then the Sun. Beyond the Sun were a further three spheres on which Mars, then Jupiter and then Saturn orbited the Earth.

## Who is known as father of trigonometry?

The first known table of chords was produced by the Greek mathematician **Hipparchus** in about 140 BC. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. This makes Hipparchus the founder of trigonometry.

### Related questions

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### How do you find a triangle inequality?

According to the triangle inequality theorem, **the sum of any two sides of a triangle is greater than or equal to the third side of a triangle**. This statement can symbolically be represented as; a + b > c. a + c > b.

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### What is half the product of the diagonals?

ANSWER. **The area of a rhombus** is half the product of its diagonals.Jun 30, 2020

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### What is the cyclic quadrilateral theorem?

**The ratio between the diagonals and the sides** can be defined and is known as Cyclic quadrilateral theorem. If there's a quadrilateral which is inscribed in a circle, then the product of the diagonals is equal to the sum of the product of its two pairs of opposite sides.

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### What does Ptolemy mean?

1 : of or relating to the second century geographer and astronomer Ptolemy of Alexandria and especially to his belief that **the earth is at the center of the universe with the sun, moon, and planets revolving around it** the Ptolemaic system.

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### How strict is Ptolemy's inequality?

- For any other four points,
**Ptolemy**'s**inequality**is strict.**Ptolemy**'s**inequality**holds more generally in any inner product space, and whenever it is true for a real normed vector space, that space must be an inner product space.

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### Does Ptolemy's theorem apply to all four points in the plane?

- However, the theorem applies more generally to any four points; it is not required that the quadrilateral they form be convex, simple, or even planar. For points in the plane,
**Ptolemy**'s**inequality**can be derived from the triangle**inequality**by an inversion centered at one of the four points.

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### What are the Ptolemaic spaces?

- The spaces where it remains valid are called the Ptolemaic spaces; they include the inner product spaces, Hadamard spaces, and shortest path distances on Ptolemaic graphs .
**Ptolemy**'s**inequality**is often stated for a special case, in which the four points are the vertices of a convex quadrilateral, given in cyclic order.

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### How do you solve the triangle inequality with three products?

- Thus the three product terms in the
**inequality**can be additively permuted to put any one of them on the right side of the**inequality**, so the three products of opposite sides or of diagonals of any one of the quadrilaterals must obey the triangle**inequality**.