Comment on New Spidron Geometry - ELEMENTS

edanet Sun, Nov 1, 2009
Istvan Lenart's Questions and my answers

I have a long note handwritten about my system what gives answer to most of these questions below.

1. In your system, do points exist?

2. In your system, do some quivalent of straight line exist? If so, are they spidrons?

3. Parts of the spidrons: do they correspond to segments or half-lines, that is, rays?

4. How many straight line-equivalents go through a point?

5. What elements of your system does the parallel postulate refer to?

Briefly (not finalized answers, but prompt):

1. New concept of geometrical point: Rotating and can be approach only never can be reached. More like a spinning Black Hole.

2. Straight infinite line In SPG is equivalent of a whole spidron with two infinite arm. If only one of the arms is finite, it is a half line, and if both, it is a segment.

3. No, more in 2.

4. It is a nice result, but quite comlicated to imagine. The answer is infinite many halflines and/or if it is a whole line, the middle of it can be seen as a "point" of crossection. Other parts also can be a place of a section-point like the one which cuts the whole spidron into two parts, related to each other like the golden section. Both parts are infinite but the measure of the two spiral are relating as Golden section.

5. postulate 5 - any spidronised regular polygon can be made this way with uncrossing arms. Conjecture: Only the regular polygons have sides what don't cross each other only in A or B once, i.e. at their "end".
Interesting: Parallel SpLines has 0 or even crossings!