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Squaring/**RP**-**RP** / Morons & Snobs?

July 2012. Dedicated to all **Circle Squarers** past and present and for the attention of most mathematicians, maths teachers, students and others interested in **recreationa**l maths:

A while ago I noted 'squaring a circle' under 'famous problems" in the Oxford Mathematics Study Dictionary. Having dealt with the Moons of Hippocrates it got my attention and, ignoring being told about the attempts over 20 centuries and the impossibility of doing it, using only a pen, compass and a straight edge I also tried my luck and have since spent many frustrating hours and a few elated minutes on it. Checking the Web I saw a temptation to call Later Century Circle Squarers, Morons! Elsewhere, I seem to faintly recall, was a similar urge to call Nitpicking Mathematicians, Snobs!

Some squarers, I believe, for all practical purposes succeeded; but not really as the issue of pi not having repeating decimals apparently does not allow such a claim. Anyhow -**SWANNIES METHODS **COVERS** **ALL** REGULAR POLYGONS** . In the examples given the equilateral triangle, the square, and the regular pentagon are called** RP**'s. Thus follow the steps in the **opposite diagram** for the circling of a triangle.

METHOD I: Circling an **RP**.

1. Draw an **RP** AB... with centre C.

2. Draw an outer semicircle on AB.

4. Draw the circumcircle circle of the **RP**.

5. Set compass to length of AD and from E mark F on the circumcircle.

6. Let CF intersect AB in G.

7. With C as centre and radius CG describe the required circle equal in area to the **RP**.**Note: Measurements from the screen are of no use. The diagrams are somewhat flattened vertically.**

**Opposite** is shown the essencial parts of a diagram wherein square AB.. is first circled using Metod I and this construction then used

METHOD II: Completing an

1. Use Method I to complete all the steps towards finding the required circle for an

2. Draw the given circle with with centre C and let it intersect CF in H.

3. Draw JHI//AB with J on CB and I on CD.

4. Extend JI its own length to K.

5. By simple construction complete the required

NOTE:

**On the right: **Both

So the above is not going to bring me fame. However, I would still like to qualify as a Circle Squarer (-

To the likely delight of some(one) I shall admit that, like a true squarer?, I bought the ruler, compass and pencils I used to generate my Methods from the 'shop around the corner' in the small town of Lady Grey (SA) where was visiting my wife.

Since my return to Port Elizabeth I have made myself a compass of the old blackboard type size and spent some more time on the quest to approach the impossible. I won't spoil anyones fun by saying more.

**Now all milli- picking ----- with time to spare, get hold of a beam compass, sharp pencil and large sheet of paper and enjoy proving me wrong; but you have to tell me to make me sulk! **

(( The story up till now is all that I originally wanted to present.

Copyright: See

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