Table of Contents

- 1 What is the shortest path between 2 points on a sphere?
- 2 What is a geodesic path?
- 3 What is the shortest distance on a sphere?
- 4 How many great circles can a sphere have?
- 5 What is the difference between geodetic and geodesic?
- 6 How do you calculate geodesic?
- 7 Which is the shortest path between two points on a sphere?
- 8 Which is the shortest path in a great circle?

## What is the shortest path between 2 points on a sphere?

The shortest path between two points on the surface of a sphere is an arc of a great circle (great circle distance or orthodrome). On the Earth, meridians and the equator are great circles.

## What is a geodesic path?

A shortest path, or geodesic path, between two nodes in a graph is a path with the minimum number of edges. If the graph is weighted, it is a path with the minimum sum of edge weights. The length of a geodesic path is called geodesic distance or shortest distance.

**What is geodesic app?**

At its core, Geodesic is a way to “like” something in the real word. Find a great restaurant or a hidden gem in your city, let everyone know. In order for the app to work it was crucial to test the design early and often.

**What are geodesics on a sphere?**

A geodesic, the shortest distance between any two points on a sphere, is an arc of the great circle through the two points. The formula for determining a sphere’s surface area is 4πr2; its volume is determined by (4/3)πr3.

### What is the shortest distance on a sphere?

great-circle distance

The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere’s interior).

### How many great circles can a sphere have?

There are an infinite number of great circles that can be drawn on any perfect sphere. The longitude lines on a globe all form great circles that pass through the same two points (the North Pole and the South Pole). The Equator is another great circle.

**Is a geodesic the shortest path?**

In geometry, a geodesic (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is commonly a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold.

**What is the shortest path in a network?**

What is the shortest path? The shortest path between two vertices in a network is the path where the sum of the weights of its edges is minimised.

#### What is the difference between geodetic and geodesic?

2 Answers. There is a substantial difference between the two: Geodesy is basically geographical surveying and measurement, often at a large scale and including longitude and latitude issues, while a Geodesic is about extending some properties of straight lines to curved and other spaces.

#### How do you calculate geodesic?

- The procedure for solving the geodesic equations is best illustrated with a fairly. simple example: finding the geodesics on a plane, using polar coordinates to.
- First, the metric for the plane in polar coordinates is. ds2 = dr2 + r2dφ2.
- Then the distance along a curve between A and B is given by. S =

**How many triangles are in a geodesic sphere?**

6 triangles

A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles.

**Are geodesics straight lines?**

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, the geodesics are great circles (like the equator).

## Which is the shortest path between two points on a sphere?

The shortest path between two points on the surface of a sphere is an arc of a great circle (great circle distance or orthodrome).

## Which is the shortest path in a great circle?

Derivation of shortest paths. To prove that the minor arc of a great circle is the shortest path connecting two points on the surface of a sphere, one can apply calculus of variations to it. Consider the class of all regular paths from a point p {\\displaystyle p} to another point q {\\displaystyle q} .

**What are the great circles of the n-sphere?**

These great circles are the geodesics of the sphere. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1.

**How is a great circle divided in two equal hemispheres?**

A great circle divides the sphere in two equal hemispheres A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. A great circle is the largest circle that can be drawn on any given sphere.