The circle and sphere are two separate terms in mathematics and physics. Even circular objects also have different properties. People are confused with its shape.

But the circle is two-dimensional, and a sphere is three-dimensional with different properties. The earth we live on will be a better example to differentiate circle and sphere.

## Circle vs Sphere

The difference between a circle and a sphere is their dimensions. The circle is a two-dimensional one, and the sphere is a three-dimensional one. A circle is a round object in the plane, and the sphere is a round object space. In the circle, the area will be calculated. But in the sphere, both the area and volume are calculated. The wheel is an example for a circle, and the tennis ball is an example for the sphere.

A shape that has all the points in the plane from the given point then is a circle. In simple, the circle is a full curve tracing by a single point. The single point is constant from all the points in the circle.

The distance between the constant point and the point in the outline of the circle is called the radius. A circle is a closed curve. Two regions in the circle may refer to the same thing, but the disc is the strict technical used word.

The sphere has its points in space. It has three dimensional namely X, Y, Z. The earth is a sphere, and the sun is the largest sphere in the solar system. Like a circle the point all connect one single point and the distance between them is the radius.

The diameter of the sphere is nothing but the longest line passing through it or twice the radius. The properties of the sphere may look the same as a circle, but the sphere is in space.

## Comparison Table

Parameters of Comparison | Circle | Sphere |
---|---|---|

Definition | The circle is a two-dimensional figure in the plane. | A sphere is a three-dimensional object in space. |

Area formula | Circle- πr2 | Sphere-4πr2 |

Components | Circle has area | Sphere has area and volume |

Volume formula | The circle has no volume | Sphere- 4/3π r3 |

Circumference | Circle- 2 π r | The sphere has no circumference |

Equation | (x−a)2+(y−b)2= r2 | (x−h)2+(y−k)2+(z−l)2=r2 |

## What is Circle?

From the Greek word Kirkos which means ring, the word circle is derived.

The circle is the best-founded object by pre-historic humans after the fire. The history of a circle is founded even before the recorded history. The circle inventions are gears that are responsible for the changes that happen in the world of science.

Geometry developed the study of the circle in mathematics, astronomy, and calculus. Many scholars who lived in the early period believed that divine and perfect is hide behind the circle.

The circle is used directly or indirectly in Indus valley civilization, ancient Egyptians, western civilizations. They used it for art to convey messages. People have a different opinions on the circle.

Some focus on the demonstration while others about its center and symbolize. The circle is religious related to infinity, unity, spirituous and etc. The compass and a halo are examples of objects in a circle used by our ancestors.

Circles have many properties. It is highly symmetric in shape. The line passing through the center of the circle will create a reflection symmetry and a rotational symmetry in every angle inside it.

The radius and circumference of a circle are directly proportional. The circle with a radius of 1 unit is called a unit circle. The three points not in the same line will form another unique circle.

## What is Sphere?

A sphere is a three-dimensional object in space. It is a solid surface with a round-like figure. If the four points are coplanar, then it is a sphere. The sphere is also considered by the passing through point and tangent to plane.

The circle and a point that is not in a plane are also referred to as spheres. The radical plane is formed when two spheres intersect in a circle. In a radical plane, the angle between spheres is a dihedral angle.

When a large circle is inclined on a sphere then both of them have an equal radius. The spheric sections are nothing but the plane sections in the sphere.

The sphere is divided into two equal parts called the hemisphere. When the plane intersects the sphere and subdivides the parts, then lunes will coincide with antipodal points in the plane

The points in the sphere are umbilicus. Every point on the outside will have an equal distance from the center constant point. The sphere does not have any surface area in the center.

The sphere geodesics are curves in nature. The mean curvature and Gaussian curvature are constant in the sphere.

## Main Differences Between Circle and Sphere

- The circle is a two-dimensional figure in the plane, and a sphere is a three-dimensional object in space.
- The area of a circle is Circle πr2, and the area of a sphere is 4πr2.
- The circle has no volume, and the volume of a sphere is 4/3π r3.
- The circumference of a circle is 2πr, and the sphere has no circumference.
- The equation of circle is (x−a)2+(y−b)2= r2, and the equation of sphere is (x−h)2+(y−k)2+(z−l)2=r2.

## References

- https://www.cambridge.org/core/journals/journal-of-applied-probability/article/distributions-on-the-circle-and-sphere/2B66EAF8748B7C59958EE03557BA8CB1
- https://www.sciencedirect.com/science/article/pii/S0305054806002942

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