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How To Construct Square Root Spiral With Compass

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  2. How To Construct Square Root Spiral With Compass Using
  3. How To Construct Square Root Spiral With Compass Pattern

A square root can be constructed with a compass and straightedge.In his Elements, Euclid (fl. 300 BC) gave the construction of the geometric mean of two quantities in two different places.

  1. On this page we show how to construct (draw) a 90 degree angle with compass and straightedge or ruler. There are various ways to do this, but in this construction we use a property of Thales Theorem. We create a circle where the vertex of the desired right angle is a point on a circle.
  2. How to construct a square root spiral? Also called the Spiral of Theodorus. The hypotenuses are supposed to be the square roots of the consecutive integers, which.


When calculators were not yet invented, it was hard for mathematicians to approximate irrational numbers. The irrational numbers was the offshoot of the discovery that the side length of the diagonal of a square with side length 1 is irrational. But how do mathematicians of the ancient time approximate a segment with length, say, ? Can they draw a segment whose length is exactly ?


With the knowledge of the Pythagorean theorem, it is possible to create a right triangle with side 1 unit making the diagonal . The diagonal can then be used as the side of another right triangle whose shorter side length is 1. This process can go on producing the figure above.

In the figure above, the diagonals produce lengths that are square root of natural numbers, so it is possible to create such segments using only the tools (compass and straightedge) known to ancient mathematicians.

How to construct square root spiral with compass quilt block

How To Construct Square Root Spiral With Compass Using

The figure above is called the square root spiral, root spiral, or spiral of Theodorus. It was said to be first constructed by Theodorus of Cyrene, a mathematician who lived in the 5th century BC. It is said that Theodorus also proved that all the square root of the natural numbers from 3 to 17 are irrational, except those which are perfect squares.

How To Construct Square Root Spiral With Compass Pattern

Image via Wikipedia