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 Waves Fig 1

At any point (A) draw a circle of any size. Find any point on the circumference (B) and draw a circle with the same radius (AB). Continue around drawing a circle at any new intersection (C etc.) on the circumference and you will create 6 divisions.

Intuitive Geometry Waves Fig 2

Find points D & E, connect them with a straight line to divide the circle in half.

Intuitive Geometry Waves Fig 3

Find & mark F & G. Extend DE. Draw a circle with centre G and radius GA.
With the same radius continue drawing new circles on the new intersections H, I, J etc. You can now draw the wave by using the circles as guides.

Intuitive Geometry Waves Fig 4

To scale the wave smaller: Find K, L, M, N & mark them. Connect K & M and extend the line. Connect C & N and extend the line. Connect L & B, Find and mark O. With centre A and radius AO draw a circle. With the same radius continue drawing circles on the new intersections P, Q, R, S etc. You can now draw the wave by using the smaller circles as guides.

You can continue the wave indefinitely. Learn more about scaling in the scaling section.

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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