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 For reasons I was unable to find out, this instrument has recently been superseded by an isosceles right triangle - called geo-triangle, solid, transparant, made of plastic - with an angular division radiating from the midpoint of the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 FreudenthalRelated topics
angular centre circle circular classic clear degree division draw find given half hypotenuse inside instrument measure misleading numbers plastic position protractor ray right ring say semicircle solid triangle well 180 midpointRelated quotes
We commemorate a man, a leader, who in the years of creation and achievement towered above his contemporaries in figure and manner, in voice and power, who worked and fought, and who suffered-as they all suffered who dared to preach socialism in an unreceptive and hostile age. He was a man who had vision, and dared all in those years to make that vision a reality; a man who inspired affection in his associates as in his own domestic circle, and who, daring all, created a lasting and durable political instrument which today 60 years after its first political success, provides the Government of this country and in so providing owes more than many are prepared to admit to the young Ramsay MacDonald.
Harold Wilson
So, ungentle reader, (as you and I value what we should ashamed-after witnessing a few minor circus-marvels-to call our "lives,") let us never be fooled into taking seriously that perfectly superficial distinction which is vulgarly drawn between the circus-show and "art" or "the arts." Let us not forget that every authentic "work of art" is in and of itself alive and that, however "the arts" may differ among themselves, their common function is the expression of that supreme alive-ness which is known as "beauty." This being so, our three ring circus is art-for to contend that the spectacle in question is not an authentic manifestation of "beauty" is as childish, as to dismiss the circus on the ground that it is "childish," is idiotic.
E. E. Cummings
We do not mechanically connect the sensation of white with the idea of light, any more than we connect the sensation of black with the idea of darkness. We admit that a black jewel, even if of a dead black, may be more luminous than the white or pink satin of its case. Loving light, we refuse to measure it, and we avoid the geometrical ideas of the focus and the ray, which imply the repetition-contrary to the principle of variety which guides us-of bright planes and sombre intervals in a given direction. Loving colour, we refuse to limit it, and subdued or dazzling, fresh or muddy, we accept all the possibilities contained between the two extreme points of the spectrum, between the cold and the warm tone.
Albert Gleizes
Like drawing a straight line – you draw a straight line and it's crooked and you draw another straight line on top of it and it's crooked a different way and then you draw another one and eventually you have a very rich thing on your hands which is not a straight line. If you can do that the it seems to me you are doing more than most people. The thing is, it is very difficult to know oneself whether one is doing that or not, whether you mean what you do; and there is the other problem of the way you do it and whether sometimes you do more than you mean or you do less than you mean. It's very good if you can establish a language where it's clear that that is what you are doing – that you do what you mean to do.
Jasper Johns
If we compare the third-person attitude of someone who simply says how things stand (this is the attitude of the scientist, for example) with the performative attitude of someone who tries to understand what is said to him (this is the attitude of the interpreter, for example), the implications ... become clear. ... First, interpreters relinquish superiority that observers have by virtue of their privileged position, in that they themselves are drawn, at least potentially, into negotiations about the meaning and validity of utterances. By taking part in communicative action, they accept in principle the same status as those whose utterances they are trying to understand. ... It is impossible to decide a priori who is to learn from whom.
Jürgen Habermas
