Properties. Spherical geometry has the following properties: Any two great circles intersect in two diametrically opposite points, called antipodal points. Any two points that are not antipodal points determine a unique great circle.

## What are lines called in spherical geometry?

Basic Points A line: a line on a sphere is called an arc due to the shape of a sphere. It is also the shortest distance between two points on the sphere . If an arc is extended, it will form a great circle. A great circle, however is the end of the lines path.

## What are the properties of spherical triangle?

The three angles of a spherical triangle must together be more than 180° and less than 540° . 7. The greater side is opposite the greater angle , if tow sides are equal their opposite angles are equal . , and if one side of the triangle 90° it is called a quadrantal triangle .

## Who is Father of spherical trigonometry?

Nasīr al-Dīn al-Tūsī

## What defines a spherical triangle?

A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the spherical analog of the planar triangle, and is sometimes called an Euler triangle (Harris and Stocker 1998).

## What is Napier’s formula?

For example, if we start with a, the first rule says sin a = cot B tan b. (The tangent of the complementary angle to B is the cotangent of B.) Similarly, the second rule says that sin a = sin c sin A. (The cosine of the complementary angle is just the sine.)

## What is the area of a spherical triangle?

The area of a spherical triangle on a sphere of radius r is equal to the spherical excess times r2. This relationship for the area of a spherical triangle generalizes to convex spherical polygons with the spherical excess being the sum of the angles – (n-2)π, where n is the number of sides of the polygon.

## What is spherical excess?

: the amount by which the sum of the three angles of a spherical triangle exceeds two right angles.

## What is spherical trigonometry used for?

Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam.

## What is the spherical excess of a spherical triangle?

On the plane, the sum of the interior angles of any triangle is exactly 180°. On a sphere, however, the corresponding sum is always greater than 180° but also less than 540°. That is, 180° < α + β + γ < 540° in the diagram above. The positive quantity E = α + β + γ – 180° is called the spherical excess of the triangle.

## How many right angles a rectangle has 5 points?

a quadrilateral with four right angles. a quadrilateral where the two diagonals are equal in length and bisect each other. a convex quadrilateral with successive sides a, b, c, d whose area is.

## What is the shape of right angle?

A vertical and a horizontal line make most common right angles. However, diagonal lines intersecting each other also form right angles. If you draw the diagonals of a square, a rhombus or a kite, the angle at the intersection is 90 degrees and is, therefore, a right angle.

rectilinear

## What is another name for 90 degrees?

Use perpendicular to describe lines, angles, and direction. In geometry a perpendicular angle is 90 degrees, a perfect L. On a compass, East and North are perpendicular to each other. The term can be used more generally to describe any steep angle.

## What is the name of 180 degree angle?

Angles that are 180 degrees (θ = 180°) are known as straight angles. Angles between 180 and 360 degrees (180°< θ < 360°) are called reflex angles.