Is a circle with infinite radius a straight line?

In Euclidean geometry, such a “circle of infinite radius” would be a straight line, but in hyperbolic geometry it is a horocycle (a curve). From the convex side the horocycle is approximated by hypercycles whose distances from their axis go towards infinity.

How do you find the straight line of a circle?

The basic equation for a straight line is y=mx+b, where b is the height of the line at x=0 and m is the gradient. The basic equation for a circle is (x−c)2+(y−d)2=r2, where r is the radius and c and d are the x and y shifts of the center of the circle away from (0, 0).

Is a radius a straight line?

RADIUS is a measure of a circle – specifically the distance between the circle and the center of the circle. A straight line-are there any other kind of line?- is not a circle. There is no radius associated with lines.

What is infinite in a circle?

In standard geometry circles (and any line segment) contain an infinite number of points. That, perhaps, makes a circle “infinite” in at least some way. A circle is also the limit of an infinite sequence of polygons as the number of sides increases to infinity.

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.

How do you draw a line in a circle in math?

How to map a line into a circle (geometry, math) – Quora. Draw the circle so that the line is tangent to the circle. Then, to map a given point of the line to a point of the circle, draw the other tangent from that point of the line to the circle. The point where this new tangent meets the circle is the point we choose …

Is a circle infinite lines?

Since there are an infinite number of lines through the center, the circle has an infinite number of lines of symmetry. When the circle is folded over a line of symmetry, the parts of the circle on each side of the line match up. This means that the parts of the circle on each side of the line must have the same area.

How do you represent infinity?

The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1655. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical.

Is there such a thing as a circle of 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.

How do you prove a line is an infinitely large circle?

Essentially, there are only two kinds of curves of constant curvature: lines (zero curvature) and circles (nonzero curvature). The statement that a line is an infinitely large circle can then be framed in terms of curvature. For each R > 0 let C R be a circle of radius R; then it has curvature 1 / R.

How do you find the curvature of a circle at infinity?

Nail down the edge of a circle. As the center gets farther and farther away, the radius gets larger, and the curvature gets smaller. When the “circle is centered at infinity” the curvature drops to zero, and the edge becomes a straight line (black).

What is the difference between circle and straight line?

On Euclidean plane, circles with very small curvature (i.e. great radius) are locally almost indistinguishable from straight lines, where straight lines are lines of zero curvature. How two definitions, of r,O -circles and of lines of constant curvature, are related?