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April 7th, 2017, 06:52 AM   #1
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Point Set Geometry

Points don't create geometry.
Geometry creates points.
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April 7th, 2017, 08:07 AM   #2
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Quote:
Originally Posted by zylo View Post
Points don't create geometry.
Geometry creates points.
Poetry?
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April 7th, 2017, 09:53 AM   #3
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Point is an undefined term in geometry. It derives its meaning from its usage definitions and axioms. Geometry is defined by the definitions and axioms. Neither creates the other, both are emergent from the definitions and axioms.

This is how a point in Euclidean geometry can be different to a point in spherical geometry despite having the same core of definitions and axioms.

Last edited by v8archie; April 7th, 2017 at 10:01 AM.
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April 7th, 2017, 03:08 PM   #4
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Quote:
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Poetry?
Mathematics.

Ref: Euclid, Euclidean Geometry; Descartes, Cartesian Geometry.

Guess these essential things have been replaced by a math major in Political Science.

EDIT
I should be more tolerant. If you've never heard of Euclid or Descartes, or read a poem, I can understand your confusion.

Last edited by zylo; April 7th, 2017 at 03:24 PM.
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April 7th, 2017, 03:24 PM   #5
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Just don't put Descartes before the horse.
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April 7th, 2017, 03:37 PM   #6
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Quote:
Originally Posted by zylo View Post
Mathematics.
Debateable.

You are doing your usual trick of assuming that everybody else is wrong simply because you don't understand the argument.

Hint: to argue coherently you first need to understand the opposing point of view. Take time to read, learn and ask for explanations. That way you don't make yourself look stupid by claiming that your gut feeling based on a couple of minutes thought is somehow more valid than hundreds of hours of study by people who have spent years getting to know and understand the subject thouroughly. Get some humility, most people have lots to be humble about and neither you nor I are exceptions to that.
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April 7th, 2017, 04:26 PM   #7
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Quote:
Originally Posted by zylo View Post
I should be more tolerant. If you've never heard of Euclid or Descartes, or read a poem, I can understand your confusion.
All ok Zylo: don't lose any sleep...

And I DO know poetry; my latest:

There once was a pretty young lass
Standing in water up to her knees
This poem does not rhyme yet
Wait till the tide comes in!
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April 8th, 2017, 04:44 AM   #8
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We have heard from Poets, Comedians, and Politicians. Amusing. Thanks. Now back to work.

Having covered how you create points from geometry (locations {Descartes) on a line (Euclid)), how do you create geometry from points?

Step 1) What is a point?

Last edited by zylo; April 8th, 2017 at 04:46 AM.
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April 8th, 2017, 04:54 AM   #9
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From the math God:
Point -- from Wolfram MathWorld
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April 8th, 2017, 05:18 AM   #10
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Quote:
Originally Posted by Denis View Post
ie, Euclid and Descartes. Thanks.

EDIT:
I still prefer "a point is a location on a line." Something has to be axiomatic, and the line seems best qualified. You can't go anywhere with a point (nothing). Nothing Set Topology.

Last edited by zylo; April 8th, 2017 at 05:30 AM.
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