A Quote by Carl Gustav Hempel
...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.
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There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.
We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
Pure geometrical regularity gives a certain pleasure to men troubled by the obscurity of outside appearance. The geometrical line is something absolutely distinct from the messiness, the confusion, and the accidental details of existing things.
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.
The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.
Next comes the realist phase ("After all, from a purely geometrical point of view a cat is only a tube with a door at the top.")
... being perpetually charmed by his familiar siren, that is, by his geometry, he neglected to eat and drink and took no care of his person; that he was often carried by force to the baths, and when there he would trace geometrical figures in the ashes of the fire, and with his finger draws lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science.
The characters and events depicted in the damn bible are fictitious. Any similarity to actual persons, living or dead, is purely coincidental.
Spatial art does not begin with a poetic mood or idea, but with construction of one or more figures, with the harmonizing of several colors and tones, or with the devaluation of spatial relationships and so on.
In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain.
The couturier should be a geometrician, for the human body makes
geometrical figures to which the materials should correspond.
The laws of Nature are written in the language of mathematics...the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.
I love the simplicity of the Cube because it's a very clear geometrical shape, and I love geometry because it's the study of how the whole universe is structured.
Geometry is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level, and the plummet. By means of optics the light in buildings can be drawn from fixed quarters of the sky. Difficult questions involving symmetry are solved by means of geometrical theories and methods.
Sit down, keep your back straight, relax and have an object on which to concentrate; you might use a candle flame, a brightly colored rock, a yantra, which is a geometrical designed specifically for the practice of concentration.
The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure.
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