By Claudi Alsina, Roger B. Nelsen
The authors current twenty icons of arithmetic, that's, geometrical shapes similar to the appropriate triangle, the Venn diagram, and the yang and yin image and discover mathematical effects linked to them. As with their prior 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 might be new even to skilled readers. in addition to theorems and proofs, the ebook includes many illustrations and it provides connections of the icons to the realm open air of arithmetic. There also are difficulties on the finish of every bankruptcy, with ideas supplied in an appendix.
The e-book will 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 through expert 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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Additional resources for Icons of Mathematics: An Exploration of Twenty Key Images (Dolciani Mathematical Expositions, Volume 45)
Show that any line through the cusp bisects its perimeter. 23. ✐ ✐ ✐ ✐ ✐ ✐ “MABK018-04” — 2011/6/1 — 17:17 — page 44 — #16 ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ “MABK018-05” — 2011/5/16 — 14:57 — page 45 — #1 ✐ CHAPTER ✐ 5 Similar Figures In the physical world, one cannot increase the size or quantity of anything without changing its quality. Similar figures exist only in pure geometry. Paul Val´ery Similar figures not only exist in geometry, they are pervasive. Our icon for this chapter on similar figures is a pair of similar triangles.
MABK018-04” — 2011/6/1 — 17:17 — page 44 — #16 ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ “MABK018-05” — 2011/5/16 — 14:57 — page 45 — #1 ✐ CHAPTER ✐ 5 Similar Figures In the physical world, one cannot increase the size or quantity of anything without changing its quality. Similar figures exist only in pure geometry. Paul Val´ery Similar figures not only exist in geometry, they are pervasive. Our icon for this chapter on similar figures is a pair of similar triangles. Equality of ratios of corresponding sides of similar triangles—Thales’ proportionality theorem—is the key to exploring similarity of figures in geometry.
The Semicircle been transformed into a curve C 0 with the same length as C but enclosing a greater area with L. As noted in the statement of Dido’s theorem, we must assume that a curve enclosing the maximum area exists. The existence of such a curve was proven formally by Karl Theodor Wilhelm Weierstrass (1815–1897). 4 The semicircles of Archimedes The Book of Lemmas (or Liber Asumptorum) is a collection of fifteen propositions and their proofs attributed to Archimedes (287–212 BCE). It survives today from an Arabic translation by Thabit ibn Qurra (836–901).