Saturday, September 02, 2006

Opinion: Axioms From Euclidean Geometry That Really Need To Go - Part 1

Welcome to the first article in a five part series.

The axiom that I hate the most is:

Axiom 3: Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.

I don't really understand this one at all. I think it's kind of dumb. This axiom has got to go!

7 Comments:

Blogger Leucipo said...

Yes, it seems not very accuratte. I propose instead:

Given any straight line segment, a circle can be drawn having the segment as radius and one choosen endpoint as center.

6:17 AM  
Blogger a spoonful weighs a ton said...

That sounds eerily similar to the original. I think you may have missed my point. I don't want to reword the axioms, as the axioms themselves are getting in the way of math. If my ultimate goal of an axiomless mathematics is to take flight, people like you are going to have to get out of the way.

8:44 AM  
Anonymous Anonymous said...

Wait a minute.

How do you know that a segment even has a center? Is that another axiom?

You can prove it using leucipo's version of the axiom. But without any such axiom, how do you prove it?

12:43 PM  
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