## What is antipode in geometry?

In mathematics, antipodal points of a sphere are those diametrically opposite to each other (the specific qualities of such a definition are that a line drawn from the one to the other passes through the center of the sphere so forms a true diameter).

## How do you find the points of a sphere?

The general equation of a sphere is: (x – a)² + (y – b)² + (z – c)² = r², where (a, b, c) represents the center of the sphere, r represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.

**What is the formula for the spherical law of sines?**

Theorem: (Spherical law of sines) sin(a) sin(A) = sin(b) sin(B) = sin(c) sin(C) .

**How do you find the distance between two points on a sphere?**

For example, haversine(θ) = sin²(θ/2). The haversine formula is a very accurate way of computing distances between two points on the surface of a sphere using the latitude and longitude of the two points.

### What is antipodal arrangement?

Answer: There is an antipodal balance of land and water on directly opposite side of the earth. It means that the continents and oceans are roughly arranged in such a way that land on the other side of the earth is balanced by water on the opposite side of the globe.

### How do you find the sides of a spherical triangle?

You could find the other two sides of the triangle using law of cosines, or you could use the Law of Sines for a spherical triangle, which is relatively easy to remember: sinαsina=sinβsinb=sinγsinc. That’s actually three equations, two of which allow you to solve for your unknown sides b and c.

**What is Girard’s theorem?**

Girard’s theorem states that the area of a spherical triangle is given by the spherical excess: , where the interior angles of the triangle are , , , and the radius of the sphere is 1. Rewriting the formula in terms of the exterior angles ‘, ‘, and ‘ gives the equivalent formula .

**How do you use haversine formula?**

Haversine formula:

- ΔlatDifference = lat1 – lat2 (difference of latitude)
- ΔlonDifference = lon1 – lon2 (difference of longitude)
- R is radius of earth i.e 6371 KM or 3961 miles.

#### What is the work of antipodal?

Antipodals are nutritive in function; it nourishes the embryo sac. Substances produced by the antipodals helps in the growth and development of the endosperm. It contains large amount of starch, lipids and proteins which are used up by the developing embryo and the endosperm.

#### What is antipode short answer?

Definition of antipode 1 : the parts of the earth diametrically opposite —usually used in plural —often used of Australia and New Zealand as contrasted to the western hemisphere. 2 : the exact opposite or contrary.

**What is the opposite of a point?**

What is the opposite of point?

meaninglessness | purposelessness |
---|---|

emptiness | worthlessness |

pointlessness | irrelevance |

aimlessness | triviality |

unimportance | inconsequence |

**What is the equation for y axis?**

x = 0

The equation of y-axis is x = 0.

## What is the radius of point sphere?

Sphere Formulas

Diameter of sphere | D = 2r, where r is the radius |
---|---|

Surface area of sphere | SA = 4πr2 Square units |

Volume of sphere | V = 4/3 πr3 Cubic Units |

## What is the sum of the sides of a spherical triangle?

The sum of the three angles in the spherical triangle PAB is 270°!

**Is haversine formula accurate?**

Haversine is accurate to round-off unless the points are nearly antipodal. Better formulas are given in the Wikipedia article on great-circle distances. Vincenty is usually accurate to about 0.1 mm. However if the points are nearly antipodal, the algorithm fails to converge and the error is much larger.

**How do you find the distance between two latitude longitude and haversine?**

### What are antipodal points in a spherical rotation?

A spherical rotation has two points that don’t move, where the rotation axis hits the sphere at a pair of antipodal points. For example, the Earth (idealized a bit) rotates on its axis, and the North and South poles don’t move.

### What are the antipodal points of the Riemann sphere?

In the first case (14.1) z and z* are antipodal points on the Riemann sphere. We can speak (following Klein) in this case about the elliptic plane as the Riemann sphere with identification of antipodal points. It is sometimes useful to use the corresponding natural elliptic metric, given by the spherical metric (line element)

**How to avoid conﬂict with the antipodal triangle?**

To avoid conﬂict with the antipodal triangle, the triangle formed by the same great circles on the oppositeside of the sphere, the sides of a spherical triangle will be restricted between 0 andπradians. The angleswill also be restricted between 0 andπradians, so that they remain interior.

**How many points determine a geodesic in spherical geometry?**

In spherical geometry, we can say “two points determine a geodesic, unless they are antipodal points, in which case there are infinitely many geodesics joining them”. This is less elegant than Euclidean geometry but fairly typical for spherical geometry, where there are often exceptions for antipodal points.