Can a sphere be infinite?
First an ideal point at infinity is added to Euclidean space so that lines (or planes) can be regarded as circles (or spheres) passing through the point at infinity (i.e., having infinite radius). Second, points are regarded as circles (or spheres) of zero radius.
Can a circle have an infinite radius?
There is no such thing as a circle of infinite radius. One might find it useful to use the phrase “circle of infinite radius” as shorthand for some limiting case of a family of circles of increasing radius, and (as the other answers show) that limit might give you a straight line.
Do spheres have infinite sides?
If you define a side as a plane that touches the object and is tangent to the object’s center of mass, then a sphere does have infinite sides. If you define a side as a face, then a sphere has no sides, by Euler’s formula (V-E+F=2).
What is infinite radius?
A horocycle can also be described as the limit of the circles that share a tangent in a given point, as their radii go towards infinity. In Euclidean geometry, such a “circle of infinite radius” would be a straight line, but in hyperbolic geometry it is a horocycle (a curve).
What is radius of sphere?
The radius of a sphere (abbreviated as the variable r or R) is the distance from the exact center of the sphere to a point on the outside edge of that sphere.
Can a sphere be flat?
A topological sphere can have a geometry that is flat except at a finite number of points: for example, the regular polyhedra are spheres that are flat except at their vertices. At the vertices themselves, the curvature becomes infinite, in such a way that its integral gives the deficit angle at that vertex.
Why is the circle infinite?
The circle is the symbol for infinity, because the circle is endless, and may be considered a polygon with an infinite number of sides. The snake or dragon with its tail in its mouth continually devouring itself and being reborn from itself is a symbol of eternity and of the cyclic nature of the universe.
Is it possible to draw a circle with zero radius?
Theoretically a point is a circle with no radius. However there is no way to draw it.
Are there infinite 3D shapes?
In geometry, an apeirogon (from the Greek words “ἄπειρος” apeiros: “infinite, boundless”, and “γωνία” gonia: “angle”) or infinite polygon is a generalized polygon with a countably infinite number of sides. Apeirogons are the two-dimensional case of infinite polytopes….Apeirogon.
| The regular apeirogon | |
|---|---|
| Internal angle (degrees) | 180° |
Can sphere have corners?
A sphere has no edges and therefore no corners. It has one curved face that goes all the way around. A square based pyramid, a triangular based pyramid and a cone have a point at the top.
Can a circle be a straight line?
Since a circle has infinite sides, the internal angles of the circle are 180 degrees, which is a straight line.
Do curved lines exist?
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. In some contexts, the function that defines the curve is called a parametrization, and the curve is a parametric curve.