ufo, animated knots
Alien to You?

From Euclid to Hilbert
Polyhedron, puzzlePolyhedron, puzzle
Polyhedron, puzzlefractal barKnots and surface

The only scary part of this site is the ufo sight.cable-planes

cable-planeAbstract Entities are cable-planes
cable-planeLiving cable-planes

saturn ray tracing A civilization is like a great river flowing through time, nourished and strengthened by many rich tributaries from other cultures. Let us project our imagination backward to a few thousand years. We are invited by the mathematics society of Greece, the birthplace of many mythical gods. We ask them a simple question: "Who created mathematics?" They respond "Mathematics begins with this half-mythical figure of Pythagoras. Science Begins with him. Western philosophy begins with him. He is even the first to use the word mathematike. Before him there was only mathemata, which meant knowledge or learning in general."
The question is answered; we may begin our real journey in this never ending rational universe.
The only rule shall be the anonymity, no last name will be mentioned, except Pappus of Alexandria.
star knots

microscopic fractal There is no royal road to geometry. The only way to a knowledge of geometry is a set of 13 books, 465 propositions, and 5 postulates. A point is that which has no part. A line is breathless length. A straight line is a line which lies evenly with the point on itself. A unit is that by virtue of which each of the things that exist is called one. A number is a multitude composed of units.
Give this person a penny, since he must make a profit out of what he learns.

microscopic fractal Eureka, eureka! Water is flowing, the goldsmith is guilty of fraud.
I shall devise engines of war and Thou shall defend Syracuse against the army and the navy of Marcellus. Romans are taking over the city and I am busy with my diagrams. A soldier is commanding me to accompany him; I say no, he is enraged; he drew his sword through me.
Place a cylinder circumscribing a sphere on my tombstone.

microscopic fractal
microscopic fractal
When I traced at my pleasure the winding to and fro of the heavenly bodies, I no longer touch the earth with my feet: I stand in presence of Zeus himself and take my fill of ambrosia, food of the gods.
The earth is at the center of the universe and does not move. The planets and stars for philosophical reasons move continuously in perfectly circular orbits. The value of pi is 3 17/120 = 3.14166 and I know the value of square root of 2.

Pappus of Alexandria, hurry up, unfortunately the great age of Greek mathematics is drawing its last breath.

microscopic fractal Fitzgerald made me famous and Blaise made me unknown. I am a mathematician, astronomer, and a famous poet. I classified algebraic equations up to the third degree in a rigorous and systematic manner and solved them through geometric means. My book, Algebra is known for its thoroughness and clarity as well as its content. It is considered as one of the masterpieces of Islamic mathematics. I am one of the creators of the most exact and perfect solar calendar.

microscopic fractal My name is Leonardo but I am better known by my nickname. I was educated in North Africa and traveled widely with my father, where I discovered the enormous advantages of the Hindu-Arabic decimal system and the use of Arabic numerals, so I introduced them into Europe. In my book Liber abaci, I showed how to compute exchanges of currency. I also posed this question: "How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?"

microscopic fractal I am a Franciscan friar living in a monastery near Palace Royal of Paris. My main interests are Philosophy, science, and mathematics. Almost every scientist in Western Europe who is active in these fields is my friend. With the approval and support of our patron, Cardinal Richelieu, my Parisian friends meet regularly in my room. The Academy of Science will be chartered in 1666, 18 years after my death. I like to work on prime numbers. People are still working on my kind of primes. I used my pulse to approximate the speed of sound. .

microscopic fractal My son you have a frail constitution, you may lie in bed until 11 a.m. First look at this fly crawling on the ceiling, then explain about Analytic Geometry... Today, November 10, 1619, is an exciting day, René is in a state of exhaustion, but he found his method... I live in the land of bears among rocks and ice, and this masculine woman of 19 wants me to meet her at 5 a.m. to show her how to draw a tangent. Why doesn't she comb her hair? I won't last more than 4 months.

microscopic fractal Marin once asked me if whether the number n = 100,895,598,169 is prime or not. I did not need many years to answer his question, without any hesitation I replied
n = 112,303
x 898,423. René claims he got his idea for Analytic Geometry from a crawling fly in his room. But several months before the publication of his book on geometry, he had my original manuscript of the Introduction. Isaac told the world that his ideas about calculus came directly from the way I draw tangents. One of my theorems is very famous.

microscopic fractal I wanted to help my father in his job, so I invented a calculator. Next time when you glance at your wrist watch, say thanks Blaise. Torricelli experimented with mercury in a tube, I did it too with many variations and great care. Sorry, if the syringe hurts, don't blame me, it was a byproduct of my experiments with mercury. My name should be on every single bus that you ride. I was the first to think of a bus system and organized a public transportation company.

microscopic fractal I was born on a Christmas Day, my father who was a farmer died before I was born. When I was young I made a toy gristmill that ground wheat to flour, with a mouse serving as motive power, and a wooden clock that worked by water. In the early years of my professorship, I became interested in optics and made the first reflecting telescope. One day Halley asked me: "What would be the curve described by the planets on the supposition that gravity diminishes as the square of the distance?" I answered immediately, "an ellipse". I revolutionized mathematics.

microscopic fractal With every lost hour a part of life perishes.... As soon as I began to learn logic, I was fascinated by its order and classification. The laws of thought are essentially algebraic in nature. I am the father of symbolic logic. I am also known as one of the two fathers of the most important branch of mathematics. My main interests are: (1) logic, (2) theology, (3) metaphysics, (4) science. In my Essais de Théodicée,I gave a rational explanation for the presence of evil in the world.

microscopic fractal My father wanted me to follow him into the church and sent me to the University of Basel to prepare for the ministry. However geometry soon became my favorite subject. The brother of James, Johann persuaded my father that I should study mathematics. I went to St. Petersburg and for 3 years I was a medical lieutenant in the Russian navy. I made some of my greatest discoveries while holding a baby on my arm with other children playing around my feet. The St. Petersburg Academy published my unpublished work for nearly 50 years after my death.

microscopic fractal Mécanique Céleste is my own work on gravitation. No one else thought of that.
Not even once, you mentioned God as the author of the universe!? Sire, I have no need of that hypothesis... I am very versatile in politics, I could be royalist as well as republican; the main thing is my well being.... My Transformation can solve many problems in mathematics such as differential equations. Engineers must know my transformation in order to make their life worth living.

microscopic fractal In my Analytical Theory of Heat I employed a trigonometric series, by means of which discontinuous functions can be expressed as the sum of an infinite series of sines and cosines. I am becoming very famous, engineers need my fast transform to filter sounds, images, data transportation, and many other things.
Napoleon is my friend, he made me a Baron. I am building the first real road from Grenoble to Turin. My other friend is Champollion. He is the one who deciphered the Rosetta Stone. My room is extremely hot, because I always feel cold.

microscopic fractal I am only three, but I must tell my father about the error in his payroll account... I need fame, an increase in my pension from the Duke, and a professorship in astronomy..... Ceres, this tiny new planet or asteroid gets moving away from the Sun. I shall use my method of least squares and my skill of numerical computation to grab that little asteroid.... I found the orbit, give me a telescope, I'll show you its exact position... If you are serious and want to learn mathematics, read all my Disquisitiones.

microscopic fractal He is a narrow-minded smug hypocrite and not even a republican. We shall not waste our valuable time to read his articles.
I started as a military engineer and went to Cherbourg to work on Napoleon's English invasion fleet. When I returned to Paris, I devoted myself to mathematics, and pioneered the study of analysis and the theory of permutation groups; I proved that the angles of a convex polyhedron are determined by its faces. In 1816 I won the Grand Prix of the French Academy of Science.

microscopic fractal The key to progress in mathematics is to study the masters and not the pupils.
In my group, you may commute freely back and forth. In Calculus you may need my test for the convergence of power series. I am the one who told Crello, why don't you make the first periodical devoted wholly to mathematical research? Call it Journal für die Reine und Angewandte Mathematik. I suffered from a pulmonary condition and was unable to find a teaching position. Two days after my death at 26, a letter came in which I was offered a teaching post at the University of Berlin.

microscopic fractal My constant companion on all my travels are my prayer book and an old, worn copy of The Disquisitiones Arithmeticae. I read this book throughout my life to keep in close touch with the wealth of deep mathematical thoughts.... I am the one who gave the correct definition of a function: "y is function of x when to each value of x in a given set X, there corresponds a unique value of y in Y." I also proved that there are an infinite number of primes in any positive arithmetic progression.

microscopic fractal I founded the set theory and showed that there are as many fractions as integers. Let me explain it. If in a classroom, all the seats are taken by students, then the set of students has the same order as the set of chairs. Here is a proof: First seat the fraction 0/1 in 0, 1/1 in 1, -1 in 2, 2 in 3, -2 in 4, 1/2 in 5, -1/2 in 6, then seat (± 3, ± 1/3, ± 3/2, and ± 2/3) the same way. Next, deal with all combinations of 4 with 1, 2, and 3 (4/3 should go to 18). This way every fraction gets an integer seat.

microscopic fractal To me, abstract entities are like living creatures... I shall risk nothing on an attempt to prove the transcendence of the number pi (this means that pi cannot be the root of a polynomial with integer coefficients). You need to wait another 9 years for pi. My forms and matrices were crucial for the formulation of quantum mechanics; my polynomials and functions are needed for the wave equation.

microscopic fractal I am the son of a village pastor, I am frail in body and shy in manner. I created a new kind of geometry, have you ever heard my kind of surface... Eight years of poverty made me write my greatest works. Now that I get paid when I teach and they call me professor, my health is gone. I am only 39 and I know my time is up. Before leaving I would like to show you a nice trick: "Rearrange these numbers and you will get different sums."

microscopic fractal My cousin served as president of France during World War I. I am clumsy and ambidextrous, my ineptitude in physical exercises is legendary. I have poor eyesight and very absent minded. I have difficulty with simple arithmetic calculation. After Carl died, it was generally thought that there never again would be a universalist in mathematics, one who is at home in all branches, pure and applied. I proved that they were wrong. My doctoral thesis was on differential equations (not on the solution, but on the existence).

microscopic fractal
black hole
black hole
In 1915 I discovered the correct field equation for general relativity before Albert but never claimed priority. In 1900 at the second international Congress of mathematicians in Paris, I presented an address in which I attempted to predict the direction of future advances in mathematics by posing 23 questions; roughly half of them remain unsolved. I am regarded as the leader of a "formalist" school of thought. In my space the elements are not points, but infinite sequences of complex numbers. I understood that not all terms in mathematics can be defined.
black holeblack holeblack holeblack hole
black holeblack holeblack holeblack hole

By the way the sum is 4100.

The Saga Continues
black hole
1 + Click + up implies that x = known
All the images of this sight
came to you from a faraway galaxy called