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.

Is the area of a circle infinite?

A circle of radius 1 centered at the origin may be placed inside of a square with corners at (-1,-1), (1,-1), (-1,1), (1,1). The area of such a square is 4, and so the area of the circle must be less than 4. All space (area) is infinite. Measurements express our understanding of such via finite rounding.

What is a circle with an 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).

Is it possible to turn a circle into a rectangle of the same area?

Changing a Circle to a Rectangle Convert the area of a circle into an rectangle shaped area of the same size. Works much the same way as a circle to square conversion but you will have to enter the width of the rectangle in addition to the circle’s diameter.

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.

Which curve is an example of infinite extent?

Transcendental Curve Such curves can have an infinite number of intersecting points together with a straight line. Moreover, they can also hold an infinite number of intersection points. A transcendental curve isn’t a polynomial based on x and y.

How do you determine the area of a circle?

The area of a circle is pi times the radius squared (A = π r²).

What is a shape with infinite sides?

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.

How is the area of a circle similar to the area of a rectangle?

Its side is r, and its “base” is equal to the circumference of the circle, 2πr. Since the area of that rectangle is twice the area of the circle, then the area of the circle is half the base times the height.

Is infinity a endless number?

infinity, the concept of something that is unlimited, endless, without bound.

What is the curve of a circle?

A common curved example is an arc of a circle, called a circular arc. In a sphere (or a spheroid), an arc of a great circle (or a great ellipse) is called a great arc.