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If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a toroid, as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings.
A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern
The compass can have an arbitrarily large radius with no markings on it (unlike certain real-world compasses). Circles and circular arcs can be drawn starting from two given points: the centre and a point on the circle. The compass may or may not collapse (i.e. fold after being taken off the page, erasing its 'stored' radius).
A 2D object traversing once around the Möbius strip returns in mirrored form. The Möbius strip has several curious properties. It is a non-orientable surface: if an asymmetric two-dimensional object slides one time around the strip, it returns to its starting position as its mirror image. In particular, a curved arrow pointing clockwise (↻ ...
A circle gradually grows larger, until it reaches the diameter of the sphere, and then gets smaller again, until it shrinks to a point and disappears. The 2D beings would not see a circle in the same way as three-dimensional beings do; rather, they only see a one-dimensional projection of the circle on their 1D "retina". Similarly, if a four ...
Malfatti's problem is to carve three cylinders from a triangular block of marble, using as much of the marble as possible. In 1803, Gian Francesco Malfatti conjectured that the solution would be obtained by inscribing three mutually tangent circles into the triangle (a problem that had previously been considered by Japanese mathematician Ajima Naonobu); these circles are now known as the ...
Penrose triangle. The Penrose triangle, also known as the Penrose tribar, the impossible tribar, [1] or the impossible triangle, [2] is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing.
Apollonian gasket; Apollonian sphere packing; Blancmange curve; Cantor dust; Cantor set; Cantor tesseract [citation needed]; Circle inversion fractal; De Rham curve; Douady rabbit; Dragon curve