View related sites
Religion and geometry have been linked throughout the centuries.
Pythagoras believed that the earth was a sphere because it was the ‘most perfect shape’. On her web pages at the University of Georgia, Kate Hobgood summarises and delves into the work of Priya Hemenway (Divine Proportion: Phi in Art, Nature and Science). She explains that the Pythagoreans believed that the circle is the parent of all shapes and that two circles with equal radii each having its centre on the other’s circumference (vesical piscis) are the building blocks for all numbers.
They attributed characteristics and intangible ideas to numbers and respective geometric diagrams, combining number, geometry and spirituality.
How does this work?
The monad (one) is god and the good, intelligence. Its circular representation has a centre, the source around which everything revolves, but which in itself is beyond understanding.
The dyad (two) involves otherness; it has audacity because it's different to one, yet anguish because it wants to be one. The dyad divides and unites, repels and attracts; it is a deity and the evil surrounding it is the door to many.
The triad (three), represented by an equilateral triangle, is the smallest area possible with a fixed perimeter: 1 + 2 = 3 and 1 + 2 + 3 = 1 x 2 x3. The triad represents wisdom, piety, friendship, peace and harmony. Its stability and strength bring balance.
These are followed by the tetrad: justice, wholeness, completion, representing the four seasons, the four ages of man and, due to its evenness, the Pythagoreans defined four as female.
Five is the symbol of life – the pentad which we now recognise as a five-point star. Representing our five fingers and five toes, this symbol has been used to ward off evil, for power and immunity, and it was used as the secret sign of the Pythagoreans. Greeks associated the pentad with the five elements of water, earth, air, fire and idea. Christians used it to signify the five wounds of Christ. When pointing downwards the symbol has been used as a sign for Satan and the Devil.
These diagrams are reminiscent, to me, of the colourful tablets offered in Shinto shrines in Japan called Sangaku (算額) that first started appearing in the early 1600s during the Edo period.
Right: Given four (equal) middle circles contained in the big circle, and a small circle inside the four. Find the radius of the big circle in terms of the radius of the small circle. Middle: Solution Left: December 1937, place Yanamachi, Matsuyama city, Ehime prefecture, Isaniwa shrine. http://atcm.mathandtech.org/ep2010/invited/3052010_18118.pdf
At this time Japan, strictly ruled by the Tokugawa shogunate, was isolated from the western world, in part as a reaction to the Spanish, Portuguese and Dutch missionaries trying to convert the population. For almost 250 years peace prevailed. The population was stable, organised into a strict social order and, despite the lack of contact with the outside world, enjoyed economic growth.
During these years Japanese art, culture and science flourished. The Kabuki opera, Noh dance, tea ceremonies, garden architecture, flower arranging, and haiku thrived. In this time of peace, the samurai looked for new goals, many excelling in the new art forms above. Others opened schools (juku) teaching writing and arithmetic. It was in these juku that the picturesque sangaku were introduced and flourished. Designed as offerings for Shinto shrines and Buddhist temples, mathematics and mathematical problems were valued as something beautiful.
In both these cases mathematics, specifically geometry, is respected and admired. Do we offer our learners the opportunity to celebrate the beauty of the mathematics they are learning? Can they take their best theorems, paint and decorate and hang them, to be admired and studied? Do we allow space for discussion about the history of mathematics and spirituality?
Join the conversation: You can tweet us @CambridgeMaths or comment below.