Thales was doubtless familiar with other theorems, not recorded by the ancients. It has been inferred that he knew the sum of the three angles of a triangle to be equal to two right angles, and the sides of equiangular triangles to be proportional.
The Eudemian Summary ascribes to Thales the invention of the theorems on the equality of vertical angles, the equality of the angles at the base of an isosceles triangle, the bisection of a circle by any diameter, and the congruence of two triangles having a side and the two adjacent angles equal respectively. The last theorem he applied to the measurement of the distances of ships from the shore. Thus Thales was the first to apply theoretical geometry to practical uses.
The theorem on the sum of the three angles of a triangle, presumably known to Thales, was proved by the Pythagoreans after the manner of Euclid. They demonstrated also that the plane about a point is completely filled by six equilateral triangles, four squares, or three regular hexagons, so that it is possible to divide up a plane into figures of either kind.
Placing your stick at the end of the shadow of the pyramid, you made by the sun's rays two triangles, and so proved that the pyramid [height] was to the stick [height] as the shadow of the pyramid to the shadow of the stick.W.W. Rouse Ball
The spider-men came first, and presented her Majesty with a table full of mathematical points, lines and figures of all sorts of squares, circles, triangles, and the like; which the Empress, notwithstanding that she had a very ready wit, and quick apprehension, could not understand; but the more she endeavoured to learn, the more was she confoundedmargaret cavendish
Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.ezra pound
Placing your stick at the end of the shadow of the pyramid, you made by the sun's rays two triangles, and so proved that the pyramid [height] was to the stick [height] as the shadow of the pyramid to the shadow of the stick.thales
Perhaps the best-known mandala-cum-plotting device in the Tantric universe is the Sri Cakra and Sri Yantra of Hindu Tantric practice, a perfectly balanced three-dimensional geometric diagram of a series of eleven interlocking and embedded triangles (also called Cakras) radiating downward and outward from a central point and enclosed by a circle and a square. The mandalas of Buddhist and Jain Tantric practice follow similar structural and dynamic principles.
The Sri Yantra is composed of two sets of triangles. One set includes four male triangles denoting the four aspects of evolved or limited consciousness. The other set includes five female triangles denoting the five vital functions, the five senses of knowledge, the five senses of action, and the five subtle and five physical forms of matter.
These two sets of triangles are superimposed to show the union of the masculine and feminine aspects of your nature. When united they make the eight lotus petals of the yantra. Four gates or doors called bhupara, surround these triangles representing the gates of the consciousness to the deeper mysteries beyond.
There is a very good saying that if triangles invented a god, they would make him three-sided