How to draw a circle without a compass?
Rough automatic draft, low quality: expect mistakes and awkward wording. It will be replaced by a better translation. Original →
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HOW TO DRAW
CIRCLE
WITHOUT COMPASSES!
There’s a geometry lesson going on.
You need to draw a circle in your notebook, but there is no compass.
You can get out of this situation by drawing a circle by hand and using only a checkered notebook. You just need to remember the numbers:
three is one, one is one, one is three.
Start drawing the circle at one of the points (A) of the intersection of the horizontal and vertical rulers of the notebook. Draw a smooth curved line from it “by eye” to the right and down, saying (aloud or mentally): three - one.
This means you move from point A to point B three cells to the right and one cell down (see figure; start moving so that your line touches the horizontal line at point A). Then from B go to C saying one to one (one square to the right and one to the bottom) and finally from C to D saying one to three. Line ABCD is a quarter circle!
From D go to E, again starting to say: three - one, this time moving three cells down and one to the left, then: one - one and one - three, moving in the same directions. The result will be similar to the DEFG circle. In the same way you will get the third quarter GHIJ (move left and up) and the quarter JKLA (up and right). If you followed this rule and never lost your way, then after point L you will end up at the starting point A. (On our figure the second half of the circle is not marked.)
After two or three attempts, you will quickly and confidently be able to draw an excellent circle without a compass.
What is this method based on?