Magic circle

Magic circles were invented by the Song Dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298). It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameter are identical. One of his magic circles was constructed from 33 natural numbers from 1 to 33 arranged on four circles , [...]

Spirograph

Spirograph is a geometric drawing toy that produces mathematical curves of the variety technically known as hypotrochoids and epitrochoids. The term has also been used to describe a variety of software applications that display similar curves, and applied to the class of curves that can be produced with the drawing equipment (so in this sense it may be regarded as a [...]

Epicycloid

 

In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called an epicycle — which rolls without slipping around a fixed circle. It is a particular kind of roulette.
If the smaller circle has radius r, and the larger circle has radius R = kr, then the parametric equations for the curve can be given by either:

or:

If k is an integer, then the [...]

Vitruvian Man

 

The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci around the year 1487 It is accompanied by notes based on the work of Vitruvius. The drawing, which is in pen and ink on paper, depicts a nude male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and [...]

Tree of life

The concept of a many-branched tree illustrating the idea that all life on earth is related has been used in science, religion, philosophy, mythology and other areas. A tree of life is variously, a) a mystical concept alluding to the interconnectedness of all life on our planet, b) a metaphor for common descent in the evolutionary sense, and c) a motif in various world theologies, mythologies and philosophies.Various trees of life are [...]

Small circle

A small circle of a sphere is the circle constructed by a plane crossing the sphere not in its center. Small circles always have smaller diameters than the sphere itself (compare great circle). Small circles cannot be parallel, because parallelism doesn’t exist in spherical geometry. They may look parallel but they are no more parallel than concentric circles on a plane.
The small circle does [...]

Great circles

A great circle of a sphere is a circle that runs along the surface of that sphere so as to cut it into two equal halves. The great circle therefore has both the same circumference and the same center as the sphere. It is the largest circle that can be drawn on a given sphere.
Great circles serve as the analogue of [...]

Squaring the circle

 

Squaring the circle is a problem proposed by ancient geometers. It is the challenge to construct a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such [...]

Monad

Monad (from Greek μονάς monas, “unit”; monos, “alone”),which according to the Pythagoreans, was a term for God or the first being, or the totality of all beings. Monad being the source or the One meaning without division.
For the Pythagoreans, the generation of number series was related to objects of geometry as well as cosmogony. According to Diogenes Laertius, from the monad evolved the dyad; from it numbers; [...]

the number 0

0 (zero) is both a number and the numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraicstructures. As a digit, zero is used as a placeholder in place value systems. In the English language, zero may also be called oh, null, nil or naught
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