[AntonioLao]

Desargues’ theorem is a theorem of projective geometry. The complicated proofs have been provided for the 2D Euclidean plane and the 3D Euclidean space. But what could be the 4D Euclidean equivalent of these proofs?

In order to show depth, many of the Renaissance paintings (starting with Leonardo da Vinci’s and Albrecht Durer’s) have been based on points at infinity of projective geometry. And modern architectural projective drawings can’t be done without all these points lying on a single line at infinity.

Projective geometry is a branch of mathematics and was discovered by the Frenchman Jean-Victor Poncelet, when he was a prisoner of war in Russia in 1813.

[Guille]

Do you have links to places where the proofs of Euclidean plane and space are?

Are there proofs for gaussian or Reimanian spaces or planes?

Anyway, if nature doesn't have 4 spacial dimension, thing which should be thought always, until a proof of the opppsoite is done, why do we need a proof for 4d Euclidean space?

[AntonioLao]

Euclid's, Gauss's or Riemann's geometry do not need any proof. They are based on their different parallel axioms.

[donschro]

Anyway, if nature doesn't have 4 spacial dimension

It would seem as though nature does have a 4th spacial dimension though likely we can't observe it. I believe ancient mathemeticians solve it's probable existence through the logical extension of the base number of spacial projection, which is a true progression in itself. They correctly identified the base number for the progression of the 4th dimension as 24, observed that the existence of the forth dimension was related to time and divided the first observable unit of time, the cycle of day and night, into 24 segments of time, 12 in the period of darkness and 12 in period of light. An hour only has 60 minutes of time composed of 60 seconds each by relatively modern definition.

Incidentally, it's fun to observe that reaching beyond the probability of spacial projection the base number for the progression of any interger to the nth power can be used to solve the progression of all integers to the same power by simple addition far faster than a modern mathemetician can multiply the numbers without using an electronic device.

Maybe I should have started a new thread.

[dleviwing]

donschro;
Time is a dimension of motion or change in spatial position of a body. It should not be confused as a spatial dimension of distance.

BTW: Welcome to ToeQuest.

[donschro]

David,
Only

[theunify]

Originally Posted by dleviwing donschro; Time is a dimension of motion or change in spatial position of a body. It should not be confused as a spatial dimension of distance.

Time can be generally defined as a particle which changes states. Any other concept foolheartily believes in absolute zero. In other words time does not exist in a vacuum, unless that vacuum is capable of changing states.

All measured time values are unique because the spatial components of the clocks that make up time measurements are unique, therefore spatial distances = time increments.

Change in space = flow of time.

[dleviwing]

theunify;
Time is only relevant within a dynamic environment. To say that “spatial distances = time increments” is pure nonsense. The 3 spatial dimensions have no relevance to the time dimension until one attempts to define relative motion.

Here are some online physics books you can refer to on the subject of Relativity. (book 6)
http://lightandmatter.com/

[theunify]

Originally Posted by dleviwing theunify; Time is only relevant within a dynamic environment. To say that “spatial distances = time increments” is pure nonsense. The 3 spatial dimensions have no relevance to the time dimension until one attempts to define relative motion. Here are some online physics books you can refer to on the subject of Relativity. (book 6) http://lightandmatter.com/

David, I'm dumbfounded, I meant spatial distances = time increments of the clocks. As in the hands of the clock. Please reread, I am sure I mentioned the word clock.

Spacial distance => does not imply motion.

[theunify]

Originally Posted by theunify David, I'm dumbfounded, I meant spatial distances = time increments of the clocks. As in the hands of the clock. Please reread, I am sure I mentioned the word clock. Spacial distance => does not imply motion.

Thanks for the books, but I happen to have quite a few good ones I got at a book sale.

The Quantum World From A to Z. by John Gribbin author of In Search of Shrodinger's Cat and Companion to the Cosmos. He has a Ph.D.~~in astrophysics from Cambridgeand is currently Visiting Fellow in Astronomy at the University of Sussex in England. He lives in Sussex. For 30 cents on the dollar I bought as many books as I could gather.

Curious and Interesting Mathematics, for $4.25
David WElls Fascinating compendium of strange facts

Science Technical Writing, A Manual of Style 514 pages, at 37 cents on the dollar.

Those books at the airport are soo tempting, do resist them, they are flimsy knockoffs.
I have one book, Instant Physics Tony Rothman Ph.D.~~,is an associate at Harvard College Observatory and teaches physics and astronomy at Bennington College. He is the author of A physicist on Madison Avenue and Science a la Mode.