Intuitive Geometry is a simple method of drawing anything using basic geometric shapes & patterns- with step by step instructions to draw them yourself using only a pencil, compass and ruler. You do not need any training in art or mathematics to use it and it can be taught to children.

Along with all kinds of other designs this Intuitive Geometry series is available in the shop as an e-book, an A4 print ready workbook and print ready posters

Intuitive Geometry Spirals Fig 1

Draw a line of any length. Draw a circle of any size on the line. Mark the centre as A and mark B on the circumference. Draw a circle with centre B and radius AB. Using radius AB continue to draw intersecting circles along the line.


Intuitive Geometry Spirals Fig 2

To draw a spiral with equal spacing draw an arch with centre B & radius AB on the right side. Find & mark C. Draw an arch with centre C and radius AC on the left side. Find & mark D. Draw an arch with centre B and radius BD on the right side. Find & mark E. Draw an arch with centre C and radius CE on the left side. Find & mark F. Draw an arch with centre B and radius BF on the right side. Find & mark G. With centre C and radius CG draw an arch on the left side.

This spiral can be continued indefinitely, just add more smaller circles as guides.


Intuitive Geometry Spirals Fig 3

To draw a growing spiral continue from Fig 1: Find C & D, mark them and connect them to divide the area in half. Find & mark E. With centre E and radius EB draw an arch on the left side. With centre B and radius BA draw an arch on the opposite side. Find and mark F. With centre F and radius FA draw an arch on the left side and mark G. With centre A and radius AG draw an arch on the right side. Find and mark H. With centre G and radius GH draw an arch on the left side.

You can continue this indefinitely by growing the spiral with an arch double the size of the previous one – use the little circles as a guide to count out the new circles for the arches.

How does it work

Overlapping Circles

Overlapping Circles Grid showing how Intuitive Geometry works

 

Waves curl into Spirals curl into a Torus

Intuitive Geometry Spirals Fig 4

A toroidal vortex

Intuitive Geometry Spirals Fig 5

Intuitive Geometry Spirals Fig 6

This is a fundamental geometric pattern of matter, it scales to any size, like a fractal, growing in octaves.

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