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By A. I. Markushevich

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10. What will the angle rx with the vertex at the origin pass to as a result of the transformation z' = Z3? Answer: Into the angle 3ex with the vertex at the origin. TO THE READER Mir Publishers would be grateful for your comments on the content, translation and design of this book. We would also be pleased to receive any other suggestions you may wish to make. Our address is: Mir Publishers 2 Pervy Rizhsky Pereulok 1-110, GSP, Moscow, 129820 USSR Printed in the Union of Soviet Socialist Republics OTHER BOOKS FOR YOUR LIBRARY LITTLE MATHEMATICS LIBRARY A.

For definiteness, we have seven rays in our drawing; all the 'angles MAB h B tAB 2 , A B 2AB 3 , ••• , B 7AP are taken to be equal (22 1; eaCh). The 53 function z' = Z2 transforms them into rays forming between themselves the angles twice as large; each of the angles M'A'B'h B 1A'B2, B 2A'B), ... , B;A'P' is equal to 45°. Let us calculate where the points Bit B 2 , B 3 , ••• , B 7 will pass to. The distances of their images B 1, B 2, B 3, ... , B; from the point A' will be equal to the squares of the distances AB h AB 2 , AB 3 , ...

It turns out that to reduce the problem of computing the velocity of the air particles in a flow streamlining the wing of an aircraft to a more simple problem of streamlining a circular cylinder, it is sufficient to make a conformal mapping of the figure hatched in Fig. 32a (the exterior of a wing section) onto the figure hatched in Fig. 32b (the exterior of a circle). Such a mapping is performed by means of a certain function of a complex variable. * We realize, of course, that in flight both the air particles and the wing of the aircraft move.

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