Category Archives: Euclid

A Short Dialogue, in the Manner of Socrates

Posted on January 24, 2026 by PlatoHagel

Socrates: Tell me, Platohagel, when you first learned of motion, how was it described to you? Platohagel: As a body moving in a straight line unless acted upon by a force. Socrates: And this straight line—where did it live? Platohagel: … Continue reading →

Posted in Curvature Parameters, Euclid, General Relativity, Interferometer | Tagged | Leave a comment

Process Fractal vs Geometry Fractals

Posted on July 19, 2012 by PlatoHagel

Let proportion be found not only in numbers, but also in sounds, weights, times and positions, and whatever force there is.Leonardo Da Vinci The Mandelbrot set, seen here in an image generated by NOVA, epitomizes the fractal. Photo credit: © … Continue reading →

Posted in Deep Play, Euclid, geometries, Giovanni Girolamo Saccheri, Heart, Non Euclidean, Quasicrystals | Tagged , , , , , , , | 15 Comments

Donald Coxeter

Posted on June 11, 2011 by PlatoHagel

Photo by Graham Challifour. Reproduced from Critchlow, 1979, p. 132. “I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts … Continue reading →

Posted in Donald Coxeter, Euclid, Non Euclidean | Tagged , , , | Leave a comment

Galileo Galilei’s Balance

Posted on May 6, 2009 by PlatoHagel

Let proportion be found not only in numbers, but also in sounds, weights, times and positions, and whatever force there is.Leonardo Da Vinci Can it be said that measure has ever left the mind of those whose age has come … Continue reading →

Posted in Books, Deep Play, Euclid | Tagged , , | 1 Comment

Who said it?

Posted on June 8, 2008 by PlatoHagel

At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small … Continue reading →

Posted in Cayley, Donald Coxeter, Euclid, Gauss, HENRI POINCARE, Riemann Sylvestor surfaces, Self Evident | Tagged , , , , , , | Leave a comment

Ueber die Hypothesen, welche der Geometrie zu Grunde liegen.

Posted on January 24, 2008 by PlatoHagel

As I pounder the very basis of my thoughts about geometry based on the very fabric of our thinking minds, it has alway been a reductionist one in my mind, that the truth of the reality would a geometrical one. … Continue reading →

Posted in Einstein, Emergence, Euclid, General Relativity, HENRI POINCARE | Tagged , , , , | Leave a comment

Housebuilding

Posted on April 13, 2007 by PlatoHagel

It all start off as “a dream” or “an idea.” Where do these come from? Dialogos of Eide This is the house similar to what we will be constructing, with some modifications of course. Most know of my time helping … Continue reading →

Posted in Blank Slate, Colour of Gravity, Deep Play, Euclid, Foundation, House Building, Library, Liminocentric, Mandalas, Raphael, School of Athens, Signatore, Topology, Toposense | Tagged , , , , , , , , , , , , , | Leave a comment

Whose who, in the School of Athens

Posted on January 29, 2007 by PlatoHagel

I was over visiting Clifford’s blog called Asymptotia this morning and notice a blog entry called, Heretics of Alexandria. Of course, what first came to mind is the “Library of Alexandria.” Clifford writes and paraphrases: This full length drama, set … Continue reading →

Posted in Alexandria, Euclid, geometries, Library, Raphael, School of Athens, Signatore, Socrates, Socratic Method, Timaeus | Tagged , , , , , , , , , , | Leave a comment

The Mathematikoi had Synesthesia?

Posted on January 28, 2007 by PlatoHagel

Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and platonism. Later resurgence of ideas similar … Continue reading →

Posted in Colour of Gravity, Complexity, Euclid, Faraday, Gauss, General Relativity, House Building, Non Euclidean, Synesthesia | Tagged , , , , , , , , , | Leave a comment

Mersenne Prime: One < the Power of two

Posted on January 7, 2007 by PlatoHagel

It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow. (The numbers on that curve are of the form x(x+1) + 41, the … Continue reading →

Posted in Computers, Cosmology, Curvature Parameters, Euclid, Euler, Imagery dimension, Mathematics, Powers of Ten, Ramanujan, Riemann Hypothesis | Tagged , , , , , , , , , | Leave a comment