By Iakov Isaevich Khurgin
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Extra info for Did You Say Mathematics?
The cat is distorted: all points have been displaced, with the sole exception of point 0 , which remains fixed. Now (Fig. 24) let us displace the entire figure of the distorted cat in parallel fashion so that it remains inside the original figure. These two consecutive transformations—nonuniform compression and parallel translation—may be regarded as a single transformation of the cat into itself. The reader can now ask himself whether under such a transformation at least one point remains fixed or whether all points of the figure have occupied new positions.
The sciences taught at school constantly undergo change. At school my parents never heard of Marx or 34 Lenin, Rutherford or Einstein, Gorky or Mayakovsky, Darwin or Popov. But the geometry of Euclid, the Pythagorean theorem, the formulas for solving quadratic equations, and the representation of the sine of a sum of two angles have all been taught to numerous generations of children, and will continue to be taught. This creates the impression of mathematics as of a fixed and finished edifice. Can you picture for a moment the physics and astronomy of the 17th century prior to Newton's discovery of the law of universal gravitation and the famous three Newtonian laws of motion, prior to the discovery of electricity and electromagnetic induction, prior to Coulomb, Volta, Ampere, and Faraday?
Now release the sheet and let it take up its original normal position. The cat will contract and find itself inside the original drawing as the fantastic distortion shown in Fig. 25. I think it will now be clear to the reader that in this complex transformation, all points of the original cat have taken up fresh positions and not a single one has remained fixed. At any rate, I have asked this question of many people and they have all stood firm in that opinion. However, our intuition has played a trick on us: 'hp assertion that, all points of the figure have been 53 Fig.