000RM.dvi
9.3 Heron triangles with consecutive sides 305 Appendix: Heron triangles with sides< 100 (a, b, c, )(a, b, c, )(a, b, c, )(a, ...
306 The area of a triangle Appendix: A famous unsolved problem Find a Heron triangle whose medians have integer lengths. This is ...
9.3 Heron triangles with consecutive sides 307 Project: Triangles whose sides and one altitude are in arithmetic progression Thi ...
308 The area of a triangle fork=1: 48 x^3 +56x^2 +16x−1=0, fork=2: 48 x^3 +44x^2 +8x−1=0, fork=3: 48 x^3 +24x−1=0. The casek=3h ...
Chapter 10 The golden section φ = √ 5+1 2 =1. 6180339887 ··· 1 The golden triangle 2 Dissection of a square 3 Dissection of a re ...
310 The golden section 10.1 The golden sectionφ A segmentABis said to be divided into the golden ratio by a pointPif AP^2 =AB·PB ...
10.2 Dissection of a square 311 10.2 Dissection of a square Show how the square should be dissected so that it can be reassemble ...
312 The golden section Resolve the paradox: How can the area increase after reassembling? A B D C Q P X Y 3 5 5 3 5 3 8 5 3 5 5 ...
10.3 Dissection of a rectangle 313 10.3 Dissection of a rectangle LetPandQbe points on the sidesABandBCof rectangleABCD. If the ...
314 The golden section 10.4 The golden right triangle The golden right triangle is the one whose hypotenuse and one leg are in t ...
10.4 The golden right triangle 315 Find the isosceles triangle of smallest perimeter that circumscribed a given semicircle. Supp ...
316 The golden section 10.5 What is the most non-isosceles triangle? Given a triangle, there are 6 ratios obtained by comparing ...
10.5 What is the most non-isosceles triangle? 317 Project: Cutting a square into three similar parts Cut a square into three sim ...
318 The golden section Exercise 1.Show thatcos 36◦=φ 2. 2.Which of the two equilateral triangles inscribed in a regular pen- tag ...
10.5 What is the most non-isosceles triangle? 319 If we assume the regular pentagon inscribed in a unit circle, the side- length ...
320 The golden section ...
Chapter 11 Constructions with the golden section 1 Construction of golden rectangle 2 Hofstetter’s compass-only construction of ...
322 Constructions with the golden section 11.1 Construction of golden rectangle ...
11.2 Hofstetter’s compass-only construction of the golden section 323 11.2 Hofstetter’s compass-only construction of the golden ...
324 Constructions with the golden section 1.C 1 =A(B), 2.C 2 =B(A), intersectingC 1 atCandD, 3.CDto intersectABat (their common ...
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