12 Axioms are Worth 12,000 Words

Subject: 12 Axioms are worth 12,000 Words

Author: Jesse Yoder <jesse@flowresearch.com >

Date: Fri, 6 Feb 1998 08:49:05 -0500

Hi everyone -

I have managed to distill my Circular Geometry down to 12 axioms (I realize that my recent posts have been somewhat lengthy), and have created a Powerpoint slide of the coordinate system together with these axioms, which I sent out separately. Unfortunately, when I copied this graphic into an email post, it disappeared in transit (which explains the blank note). However, here are the axioms, in case you can't open a Powerpoint slide.

1. A Point is the smallest allowable unit of measurement within a system of measurement.

2. Every Point has area.

3. A Point is a circular figure that is considered to be indivisible for the measurement being made.

4. A Line is the path of a Point in motion.

5. Every Line has width. The width of a Line is the diameter of the Point being used for a particular measurement.

6. Every measurement involving Points and Lines is relative top a system of measurement in which the reference of the terms 'Point' and 'Line' is fixed for the purposes of that measurement. The reference of 'Point' determines the degree of precision used in the measurement.

7. In the Coordinate System of Circular Geometry, there is an X axis consisting of unit Circles laid end to end in an east to west direction, each with a value of one round inch. Likewise, there is a Y axis consisting of unit Circles laid end to end in a north to south direction, each with a value of one round inch. The Point of intersection of these Circles creates the integers 0, 1, 2, 3, etc.

8. To find the area of a Circle, which is the number of round inches in the Circle, use the formula 4 * r * r, where r is the radius of a Circle. Alternatively, use d * d, where d is the diameter of the Circle.

9. A Point lies on the Line, not in the Line. Finitely many Points lie on any given Line.

10. A Circle is a continuous closed geometric figure that is the path generated by rotating a Point around a fixed Point until it intersects its starting position.

11. Every Circle has an inside Diameter (ID) and an outside Diameter (OD). The inside Diameter being and ends at the inside edge of the Circle. The outside Diameter begins and ends at the outside edge of the Circle. The inside Area is calculated by taking 'd' to be the Inside Diameter in the formula d * d. The outside Area includes the Circle boundary, and is calculated by taking 'd' as the outside Diameter in the formula d * d.

12. A Plane is the path generated by moving a Line through Space. Just as a Line has width, a Plane has a depth equal to the width of the Line.

Note: Special thanks to John Conway for helpful comments and suggestions. Special thanks also to Kirby Urner, K. K. G. Yau, Floor Lamoen, Candice Hebden, Helena Verill, and DGoncz for helpful comments and suggestions.

-- Jesse Yoder

Additional note: If you can't open the Powerpoint slide, and you want to see the Coordinate System, I will fax it to you if you email me your fax number. Thanks in advance for any comments you have on this.

***

To see the original post, go to:

http://forum.swarthmore.edu/epigone/geometry-research/khunfangprax

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