Intuitive Geometry is a simple method of drawing anything using overlapping circles. Once you master the method’s 8 principles (circle, square, triangle, hexagon, pentagon, spirals, waves, scaling) you can apply them intuitively and draw anything.

Intuitive Geometry Pentagon Method Icons

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Pentagon Step by Step Instructions

Intuitive Geometry Pentagon Fig 1

Draw any finite line, find A & B and mark them. Draw a circle with centre A and radius AB & centre B radius AB. Find and join C & D. Draw an arch with centre D and radius DA. Find E, F and G, mark them.

Intuitive Geometry Pentagon Fig 2

Join E through G to find H, Join F through G to find I. Mark H, I and J. With Radius AB draw two arches, one with centre I and the other with centre H. Join A & I, I & J, J & H and H & B. You have drawn a Pentagon.

Intuitive Geometry Pentagon Fig 3

Find K & L, mark them. Connect B through K and A through L. Find & mark M. Extend I through M and H through M. You have created 10 divisions.

Intuitive Geometry Pentagon Fig 4

Draw a circle with centre M and radius MJ. Find and mark N, O, P, Q and R.
Connect N O P Q R to form the second pentagon.

Intuitive Geometry Pentagon Fig 5

Find & Mark S, T, U, V, W, X, Y , Z, Aa, Bb. You have created 20 divisions. Extend the lines to the circumference of the circle & connect the new pentagons: S U W Y Aa & T V X Z Bb.

Intuitive Geometry Pentagon Fig 6

Find the new intersections Cc, Dd etc. and connect them through centre M to create a total of 40 divisions. You can continue with this method to create 80, 160, 320 etc. divisions.

The Dodecahedron

Intuitive Geometry Pentagon Fig 7

Draw any finite straight line AB. Draw a circle of any size on the line. Using the same radius mark 6 divisions on the circumference of the circle. Connect the divisions through the middle to create CF and DE. Using the same radius find and circle G, H, I, J, K, L, M, N, O, P, Q and R.

Intuitive Geometry Pentagon Fig 8

Connect R & I, R & J, R & M and R & N. Repeat this pattern of connection for points G, I, L, N and P: GP, GK, GL, etc. Find S & T, mark them and find the others. Thicken the rest of the lines to show the dodecahedron.

How does it work

Overlapping Circles

Overlapping Circles Grid showing how Intuitive Geometry works

The Pentagon Net

Draw a line from K through A. Using Radius A1 find 2. Using radius AK draw a circle with centre 2. Create a pentagon using method 2. Repeat the process all around to create the 5 pentagons that form at the base of the original one.

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