Download Icons of Mathematics: An Exploration of Twenty Key Images by Claudi Alsina, Roger B. Nelsen PDF
By Claudi Alsina, Roger B. Nelsen
The authors current twenty icons of arithmetic, that's, geometrical shapes comparable to the precise triangle, the Venn diagram, and the yang and yin image and discover mathematical effects linked to them. As with their past books (Charming Proofs, When much less is More, Math Made Visual) proofs are visible each time possible.
The effects require not more than high-school arithmetic to understand and lots of of them may be new even to skilled readers. in addition to theorems and proofs, the booklet comprises many illustrations and it provides connections of the icons to the area open air of arithmetic. There also are difficulties on the finish of every bankruptcy, with ideas supplied in an appendix.
The booklet may be utilized by scholars in classes in challenge fixing, mathematical reasoning, or arithmetic for the liberal arts. it might probably even be learn with excitement by means of specialist mathematicians, because it used to be via the individuals of the Dolciani editorial board, who unanimously suggest its publication.
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Read or Download Icons of Mathematics: An Exploration of Twenty Key Images (Dolciani Mathematical Expositions, Volume 45) PDF
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Extra resources for Icons of Mathematics: An Exploration of Twenty Key Images (Dolciani Mathematical Expositions, Volume 45)
Sample text
2. Here we present a geometric proof [Nelsen, 2002b] based on the Pythagorean theorem. In Proposition 31 of Book VI of the Elements, Euclid writes: In right-angled triangles the figure on the side opposite the right angle equals the sum of the similar and similarly described figures on the sides containing the right angle. For similar figures on the sides, we now use semicircles. 8. 8. 8c, B2 D A2 C C2 . Together the equations yield ACA1 CA2 D A1 CC1 CA2 CC2 , which simplifies to A D C1 CC2 D C .
Imagining Pythagoras Portraits and busts of mathematicians from antiquity arise from the imaginations of artists and sculptors. The fame of the Pythagorean theorem through the centuries has motivated a great collection of images of its namesake. 18 we see a bust from the Capitoline Museums in Rome, an illustration from the Nuremburg Chronicle (1493), detail from Rafael’s The School of Athens (1509), and a postage stamp issued by San Marino in 1982. 18. 1. 1 is the 3-4-5 right triangle. (a) Are there other right triangles whose sides are in arithmetic progression?
Sangaku are Japanese geometry theorems that were often written on wooden tablets during the Edo period (1603–1867) and hung on Buddhist temples as offerings. 21. Show that the area of the shaded triangle is equal to the area of the shaded square. 21. 5. 22. 22. vertex to a vertex of the square on the opposite side as shown. Which has the larger area, triangle ABH or quadrilateral HIJC ? 6. 23. Then the midpoints Q and S of the segments BD 0 and B 0 D together with the centers R and T of the original squares form another square QRS T .