Notitia Dignitatum

The Notitia Dignitatum is a unique document of the Roman imperial chanceries. One of the very few surviving documents of Roman government, it details the administrative organisation of the eastern and westernempires, listing several thousand offices from the imperial court down to the provincial level. It is usually considered to be up to date for the Western empire in the 420s, [...]

Taijitu

Taijitu (a Chinese word that translates roughly as ‘diagram of ultimate power’) is a term which refers to any of the Chinese symbols for the concept of yin yang, and is sometimes extended to similar geometric patterns used historically by various cultures. The most recognized form is composed of two semi-circular teardrop-shaped curves of different colors, or [...]

Sesame street/Philip Glass: Geometry of 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 [...]

ISO 216

ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today. It is the standard which defines the commonly available A4 paper size. The underlying principle is that when rectangles with width/length ratio  are cut or folded in half the rectangles thus formed retain the original width/length ratio.
 
The international ISO standard is based on the German DIN standard [...]

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 [...]

compasses

 

A compass, magnetic compass or mariner’s compass is a navigational instrument for determining direction relative to the earth’s magnetic poles. It consists of a magnetized pointer (usually marked on the North end) free to align itself with Earth’s magnetic field. The face of the compass generally highlights the cardinal points of north, south, east and west. The compass greatly improved the safety and efficiency [...]

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 [...]