1830-1930: A Century of Geometry by L. Boi, D. Flament, Jean-Michel Salanskis PDF

By L. Boi, D. Flament, Jean-Michel Salanskis

ISBN-10: 0387554084

ISBN-13: 9780387554082

ISBN-10: 3540554084

ISBN-13: 9783540554080

Within the first 1/2 the nineteenth century geometry replaced extensively, and withina century it helped to revolutionize either arithmetic and physics. It additionally placed the epistemology and the philosophy of technological know-how on a brand new footing. In this quantity a valid evaluation of this improvement is given via prime mathematicians, physicists, philosophers, and historians of technology. This interdisciplinary technique supplies this assortment a distinct personality. it may be utilized by scientists and scholars, however it additionally addresses a basic readership.

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Additional resources for 1830-1930: A Century of Geometry

Sample text

Looking at the three functions f, g, and h we have considered so far, we notice a progressive ‘deterioration’: f simply failed to preserve distances (mapping ABCD to a bigger rectangle), g failed to preserve right angles (but at least sent parallel lines to parallel lines), while h did not even preserve straight lines (it mapped AB and CD to curvy lines). Now that we have seen how ‘bad’ some (in fact most) functions can be, we may as well ask how ‘good’ they can get: are there any functions that preserve distances (therefore angles and shapes as well), satisfying |AB| = |A′ B ′ | for every two points A, B on the plane?

Notice at this point that any two vectors of equal length and same direction and sense are one and the same, while any two vectors of equal length and same direction might be either one and the same or opposite of each other. 1 Mirrors create equals. Anyone who has ever successfully looked into a mirror is aware of this simple, as well as deep, natural phenomenon. Moreover, the closer you stand to a mirror, the closer you see your image in it -- another simple truth that even your cat is likely to be painfully aware of!

6. Perhaps we could have achieved some greater precision with the use of more precise drawing and instruments, but such great precision will probably not be possible when you take your exam anyway... Let us now see how things work out for A ″ , the clockwise image of A = (2, 1). 7). 7): our estimate (in fact our drawing) worked perfectly this time -- it happens! 34y) in the counterclockwise case. You should now get a bit more practice by near-matching formula outcomes and geometrical estimates for B ′, C′, B″ , and C″ , redrawing the image triangles A′B ′C ′ and A″ B ″ C ″ in case you are not happy with our drawing: good luck!

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1830-1930: A Century of Geometry by L. Boi, D. Flament, Jean-Michel Salanskis


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