Triangle Quotes - page 2
As yonder tower outstretches to the earth
The dark triangle of its shade alone
When the clear day is shining on its top;
So, darkness in the pathway of man's life
Is but the shadow of God's providence,
By the great Sun of wisdom cast thereon;
And what is dark below is light in heaven.
John Greenleaf Whittier
...by action on man all known force may be measured. Indeed, few men of science measured force in any other way. After once admitting that a straight line was the shortest distance between two points, no serious mathematician cared to deny anything that suited his convenience, and rejected no symbol, proved or unproveable, that helped him to accomplish work. The symbol was force, as a compass-needle or a triangle was force.
Henry Adams
As long as he could whisper, he would go on as he had begun, bluntly refusing to meet his creator with the admission that the creation had taught him nothing except that the square of the hypotenuse of a right-angled triangle might for convenience be taken as equal to something else. Every man with self-respect enough to become effective, if only as a machine, has had to account to himself for himself somehow, and to invent a formula of his own for his universe, if the standard formulas failed.
Henry Adams
The dangers to which we are exposed from our Women must now be manifest to the meanest capacity in Spaceland. If even the angle of a respectable Triangle in the middle class is not without its dangers; if to run against a Working Man involves a gash; if collision with an officer of the military class necessitates a serious wound; if a mere touch from the vertex of a Private Soldier brings with it danger of death; - what can it be to run against a Woman, except absolute and immediate destruction? And when a Woman is invisible, or visible only as a dim sub-lustrous point, how difficult must it be, even for the most cautious, always to avoid collision!
Edwin Abbott Abbott
You mention the circle and I agree with your definition.... why does the circle fascinates me? It is (1) the most modern form, but asserts itself unconditionally, (2) a precise but inexhaustible variable, (3) simultaneously stable and unstable, (4) simultaneously loud and soft, (5) a single tension that caries countless tensions within it. The circle is the synthesis of the greatest oppositions. It combines the concentric and the eccentric in a single form, and in balance. Of the three primary forms (triangle, square, circle), it points most clearly to the fourth dimension.
Wassily Kandinsky
First then I will set out the very first theorem which became known to me by means of mechanics, namely that
Any segment of a section of a right angled cone (i.e., a parabola) is four-thirds of the triangle which has the same base and equal height,
and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]...
Archimedes
The classic instrument to measure drawn angles and to draw angles of a given measure is the protractor - essentially half a circular ring, subdivided by ray segments into 180 degrees. For reasons I was unable to find out, this instrument has recently been superseded by an isosceles right triangle - called geo-triangle, solid, transparant, made of plastic - with an angular division radiating from the midpoint of the hypotenuse to the other sides. Well, inside the triangle half a circle with the midpoint of the hypotenuse as its centre is indicated, and from the position of the degree numbers it becomes clear that it is the semicircle that really matters. One is inclined to say "an outrageously misleading instrument"...
Hans Freudenthal
Rapidly going over what I could recall of Jim Bursley's information about pathological curves confirmed the conjecture. The snowball curve, derived from an equilateral triangle, is a perimeter of infinite length enclosing a finite area. The angles or points of the perimeter are uncountable. An equilateral triangle projected integrally in the third dimension is a triangular pyramid of equal surfaces. The three-dimensional snowflake derived from this pyramid--hence its diamantine appearance--is a finite volume enclosed in a surface of infinite area. The convolutions of such a surface, to be gathered around its defined content extrude a number of discrete angles or points beyond all possibility of computation. The pressure on each point is infinitesimal, unmeasurably small; the total external pressure exerted on any part of the surface is an aggregate of infinitesimal values, itself infinitesimal.
William Grey Walter
Filming 'Eclipse' - Eclipse was my favorite book so I was really excited to start filming the movie. I just love that it's the height of the love triangle. 'Twilight' develops Edward and Bella's relationship, 'New Moon' develops Jacob and Bella's and in 'Eclipse,' the three of them are physically together.
Taylor Lautner
Nelson's challenge was that he was outnumbered. His strategy was to risk his lead ships in order to break the coherence of his enemy's fleet. With coherence lost, he judged, the more experienced English captains would come out on top in the ensuing melee. Good strategy almost always looks this simple and obvious and does not take a thick deck of PowerPoint slides to explain. It does not pop out of some "strategic management" tool, matrix, chart, triangle, or fill-in-the-blanks scheme. Instead, a talented leader identifi es the one or two critical issues in the situation-the pivot points that can multiply the effectiveness of effort-and then focuses and concentrates action and resources on them.
Richard Rumelt
Recall that democratic regimes in an exchange society are at one corner of the political triangle while totalitarian regimes with the coercive society they have constructed are at another. They therefore are at opposing ends of one side of the triangle, which is a continuum ranging from Freedom to Power.
Rudolph Rummel
Currency competition and free banking might increase the efficiency of the financial system, and bring some small triangle welfare gains. But the key question is whether their adoption would improve macroeconomic performance. Even though Salin argues (p. 281) that ‘the best system is that which produces the least inflation', fluctuations in output are also expensive.
Hayek states that the adoption of his proposal would end recessions. There is absolutely no reason to believe that. Nineteenth century history is evidence that free banking and currency issue, in the wrong legal and regulatory framework, can produce rather than reduce instability. The proponents of free banking and currency issue in this volume do not go much beyond a general belief in competition in justifying their views; they have certainly not explored the necessary legal and regulatory environment in any detail.
Stanley Fischer
The unerring signs of truth and falsehood are clear, distinct consistency and contradiction. This is also the case with revelation, in so far as that it must, in common with other truths, be free from contradiction. And just as little as miracles can prove that twice two are five or that a triangle has four angles, can a contradiction lying in the history and dogmas of Christianity be removed by any number of miracles.
Hermann Samuel Reimarus
The method of exhaustion was not discovered all at once; we find traces of gropings after such a method before it was actually evolved. It was perhaps Antiphon. the sophist, of Athens, a contemporary of Socrates, who took the first step. He inscribed a square (or, according to another account, a triangle) in a circle, then bisected the arcs subtended by the sides, and so inscribed a polygon of double the number of sides; he then repeated the process, and maintained that, by continuing it, we should at last arrive at a polygon with sides so small as to make the polygon coincident with the circle. Thought this was formally incorrect, it nevertheless contained the germ of the method of exhaustion.
Thomas Little Heath
