Titlebook: Mathematics is Beautiful; Suggestions for peop Heinz Klaus Strick Book 20211st edition The Editor(s) (if applicable) and The Author(s), und

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惊惶

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冬眠

Sum of Spots,ally, the dice are labeled in such a way that the sum of spots of opposite surfaces add up to 7, that is, 7 = 1 + 6 = 2 + 5 = 3 + 4. To make a dice, you can use different dice nets. The best known is the shape of a lying cross, but ten other shapes are also possible.

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Kissing Circles,knowledge of trigonometric theorems, especially the law of cosines and the law of sines. For the problem of four circles touching each other (“kissing circles”), Descartes discovered a remarkable formula that can be used to calculate the radius of the circles touching three given circles.

Morose

Sums of Powers of Consecutive Natural Numbers,ulas for calculating the sum of the first . square numbers or cube numbers can be derived. In this chapter, further methods for calculating the sum of the powers of natural numbers will be presented, which have been discovered and developed over the centuries by various mathematicians.

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Heinz Klaus Strickn theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at

Kinetic

Heinz Klaus Strickexpressing the effective behavior of the given nonlinear composites in terms of the behavior of suitably chosen “linear comparison” composites. This allows the use of classical bounds and estimates (e.g., Hashin-Shtrikman, self consistent approximations) for linear materials to generate correspondin