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 of differentiating circles and spheres.
Key Takeaways
- Circles are two-dimensional shapes, while spheres are three-dimensional objects.
- The area of a circle is calculated using πr², whereas the surface area of a sphere is calculated using 4πr².
- Circles have only one edge, while spheres have no edges or vertices.
Circle vs Sphere
Circle is a two-dimensional shape and a round object of the plane, where the area can be calculated from. It is a full curve traced by a single point. Sphere is a three-dimensional shape that is found in space, consists of three dimensions which are X, Y, and Z, and includes a diameter and area.
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 traced 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 strictly technical word used.
The sphere has its points in space. It has three-dimensional, namely X, Y, and Z. The earth is a sphere, and the sun is the largest sphere in the solar system. Like a circle, the points connect to one 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?
The word circle is derived from the Greek word Kirkos which means ring.
The circle is the best-founded object by pre-historic humans after the fire. The history of a circle is founded even before 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 the divine and perfect hid behind the circle.
The circle is used directly or indirectly in Indus valley civilization, ancient Egyptians, and western civilizations. They used it for art to convey messages. People have different opinions on the circle.
Some focus on the demonstration, while others are about its centre and symbolize. The circle is religiously related to infinity, unity, spirituous, 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 centre 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. A 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 passing also considers the sphere through a point and tangent to a plane.
A 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, both 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 the umbilicus. Every point on the outside will have an equal distance from the constant centre point. The sphere does not have any surface area in the centre.
The sphere geodesics are curves in nature. The mean curvature and Gaussian curvature are constant in the sphere.
Main Differences Between Circle and Sphere
- A 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.
- 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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