Triangles on Earth Exceed 180 Degrees

The idea that space and time can be curved or warped is fairly recent. For more than 2,000 years the axioms of Euclidean geometry were considered to be selfevident. As those of you who were forced to learn geometry at school may remember, one of the consequences of these axioms is that the angles ot a triangle add up to 180 degrees. However, in the last century people began to realise that other forms of geometry were possible in which the angles of a triangle need not add up to i8o degrees...

 Flatland

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe:" but now my mind has been opened to higher views...

 We Must Learn the Language of Nature

Philosophy is written in that great book which ever lies before our gaze—I mean the universe—but we cannot understand if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles and Other geometrical figures, without the help of which it is impossible to conceive a single word of it, and without which one wanders in vain through a dark labyrinth.

 Learning to Read Nature

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

 The Circle of the Brain cannot be Squared

A Circle round divided in four partsHath been great Study 'mongst the men of Arts;Since Archimed's or Euclid's time, each BrainHath on a Line been stretched, yet all in Vain;And every Thought hath been a Figure set,Doubts Cyphers were, Hopes as Triangles met;There was Division and Subtraction made,And Lines drawn out, and Points exactly laid,But none hath yet by Demonstration foundThe way, by which to Square a Circle round:For while the Brain is round, no Square will be,While Thoughts divi...