A Quote by Willy Ronis
A fine image is geometry, modulated by the heart
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The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.
I need geometry to set the grammar of the image expressive language . The structural skeleton, the composition and the geometric layout provide a perspective from which one can read the image; otherwise we would do what Dadaists did when they put words in a little bag and then took them out at random in order to compose a poem.
The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?
In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God.
The human heart likes a little disorder in its geometry.
The idea of a spiritual heart transplant is a vivid image to me; once you have the heart of somebody else inside you, then that heart is there. Jesus' heart is inside me, and my heart is gone. So if God were to place a stethoscope against my chest, he would hear the heart of Jesus Christ beating.
Break my heart? Is that what you just said? I have news for you; you didn't break my heart. My heart's fine. My heart's in the best shape of its life. You know what you did to me? You took an AK-47 and blew my soul open.
He loved, beneath all this summer transiency, to feel the earth's spine beneath him; for such he took the hard root of the oak tree to be; or, for image followed image, it was the back of a great horse that he was riding, or the deck of a tumbling ship -- it was anything indeed, so long as it was hard, for he felt the need of something which he could attach his floating heart to; the heart that tugged at his side; the heart that seemed filled with spiced and amorous gales every evening about this time when he walked out.
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.
Abstraction didn't have to be limited to a kind of rectilinear geometry or even a simple curve geometry. It could have a geometry that had a narrative impact. In other words, you could tell a story with the shapes. It wouldn't be a literal story, but the shapes and the interaction of the shapes and colors would give you a narrative sense. You could have a sense of an abstract piece flowing along and being part of an action or activity. That sort of turned me on.
Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics - these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?
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