Triangle Quotes (8 quotes)

Astronomy was thus the cradle of the natural sciences and the starting point of geometrical theories. The stars themselves gave rise to the concept of a point; triangles, quadrangles and other geometrical figures appeared in the constellations; the circle was realized by the disc of the sun and the moon. Thus in an essentially intuitive fashion the elements of geometrical thinking came into existence.

I just looked up at a fine twinkling star and thought that a voyager whom I know, now many a days sail from this coast, might possibly be looking up at that same star with me. The stars are the apexes of what triangles!

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

— Euclid

Its immediate significance was as a currency, for it closed the triangle linking spirits, slaves, and sugar. Rum could be used to buy slaves, with which to produce sugar, the leftovers of which could be made into rum to buy more slaves, and so on and on.

One of the grandest figures that ever frequented Eastern Yorkshire was William Smith, the distinguished Father of English Geology. My boyish reminiscence of the old engineer, as he sketched a triangle on the flags of our yard, and taught me how to measure it, is very vivid. The drab knee-breeches and grey worsted stockings, the deep waistcoat, with its pockets well furnished with snuffof which ample quantities continually disappeared within the finely chiselled nostriland the dark coat with its rounded outline and somewhat quakerish cut, are all clearly present to my memory.

That mathematics do not cultivate the power of generalization,;
will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction.
To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Keplers laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometrythe great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of themis a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.

The Hypotenuse has a square on,

which is equal Pythagoras instructed,

to the sum of the squares on the other two sides

If a triangle is cleverly constructed.

which is equal Pythagoras instructed,

to the sum of the squares on the other two sides

If a triangle is cleverly constructed.

The smallest particles of matter were said [by Plato] to be right-angled triangles which, after combining in pairs, ... joined together into the regular bodies of solid geometry; cubes, tetrahedrons, octahedrons and icosahedrons. These four bodies were said to be the building blocks of the four elements, earth, fire, air and water ... [The] whole thing seemed to be wild speculation. ... Even so, I was enthralled by the idea that the smallest particles of matter must reduce to some mathematical form ... The most important result of it all, perhaps, was the conviction that, in order to interpret the material world we need to know something about its smallest parts.

*[Recalling how as a teenager at school, he found Plato's*Timaeus*to be a memorable poetic and beautiful view of atoms.]*