Christian Hesse's Warum Mathematik glücklich macht - 151 verblüffende PDF

By Christian Hesse

ISBN-10: 3406606083

ISBN-13: 9783406606083

Wie die Liebe und die Musik hat Mathematik die Gabe, Menschen glücklich zu machen. Angesichts ihrer oft kargen Darreichungsform eine kühne Behauptung? Dafür, dass sie dennoch stimmt, tritt der Mathematiker und Mathematik-Belletrist Christian Hesse in seinem neuen Buch den Beweis an - in 151 erstaunlichen und gewitzten Geschichten. Warum haben Tiger Streifen, Dalmatiner Punkte und Elefanten nichts von beidem? Warum haben manche Heuschreckenarten Lebenszyklen, deren Länge immer Primzahlen sind? Wie ist es möglich festzustellen, dass Homer die Odyssee nicht geschrieben hat? Diese und viele andere Fragen kann die Mathematik beantworten, und wie sie dabei vorgeht und vor allem, wie der Autor dieses Vorgehen darstellt, das verfolgt der Leser mit Faszination, bisweilen Erstaunen und immer mit Vergnügen.

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The angle θab is the angle between the first and second vector, and thus b·a = = = = |a||b| cos θba ab cos(−θab ) ab cos(θab ) a·b . ) We thus see that order does not matter, or more formally, that the dot product is commutative. Let us look at some special cases 1. a is perpendicular to b. In that case θ = 90◦ = π/2, and the cosine is zero: a · b = 0. 6. THE SCALAR OR DOT PRODUCT 23 2. , θ = 0. a · a = a2 . For that reason one sometimes writes a2 for a2 . Also a= √ a·a . 3. i·i=j·j=k·k=1 , i·j=j·k=k·i=0 .

2 3 = 4 the standard form of L is z − 12 x + 31 y−7 = = 2 3 −2 3 Point A: − 13 , 7, 21 , position vector of A: − 31 i + 7j + 12 k. 12. 15: Example: Find the Cartesian equations of a straight line L through the point a = i − 2j + k in the direction of the vector b = −2j + 3k. i − 2j + 3k). This gives the following Cartesian equations of L: x−1 z−1 y+2 = = (= λ) 0 −2 3 29 30 CHAPTER 3. 1 Assumed knowledge First principles definition If y = f (x) and x increases from x to x + δx then the change in y is give by δy = f (x + δ) − f (x), see Fig.

1: Integrate 4x3 . Solution: 4x3 = d(x4 ) , so dx 4x3 dx = x4 + c This type of integration is called an indefinite integral. We always get a constant of integration c for an indefinite integral. Note: The result of f (x)dx is another function of x. Many of the integrals in the formula book were obtained this way, Some examples: d sin x = cos x dx 1 d ln x = dx x d(eax ) = aeax dx d(sin−1 x) 1 =√ dx 1 − x2 cos xdx = sin x + c 1 dx = ln x + c x 1 eax dx = eax + c a dx √ = sin−1 x + c 1 − x2 43 44 CHAPTER 5.

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Warum Mathematik glücklich macht - 151 verblüffende Geschichten by Christian Hesse


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