000RM.dvi
222 Pythagorean triples Project: Two pairs of primitive Pythagorean triples with almost equal perimeters In a class in Number Th ...
6.5 Dissecting a rectangle into Pythagorean triangles 223 Project: Cross number puzzle on primitive Pythagorean triples^1 123 4 ...
224 Pythagorean triples ...
Chapter 7 The tangrams 1 The Chinese tangram 2 A British tangram 3 Another British tangram Project ...
226 The tangrams 7.1 The Chinese tangram It is known that exactly 13convexpolygons can be formed from the tangram.^1 Show them.^ ...
7.2 A British tangram 227 7.2 A British tangram The seven pieces of the puzzle can be fitted together as shown in the figure to ...
228 The tangrams 7.3 Another British tangram Ten pieces of the puzzle can be fitted together as shown in the figure to make 4 × ...
7.3 Another British tangram 229 Project Show how to dissect a 3-4-5 triangle into 4 pieces that may be rearranged into a square. ...
230 The tangrams ...
Chapter 8 The classical triangle centers 1 The centroid 2 The cirumcenter and the circumcircle 3 The incenter and the incircle 4 ...
232 The classical triangle centers The following triangle centers have been known since ancient times. We shall adopt the follow ...
8.2 The circumcircle and the circumcircle 233 8.2 The circumcircle and the circumcircle The perpendicular bisectors of the three ...
234 The classical triangle centers 8.3 The incenter and the incircle The internal angle bisectors of a triangle are concurrent a ...
8.4 The orthocenter and the Euler line 235 8.4 The orthocenter and the Euler line The orthocenterHis the intersection of the thr ...
236 The classical triangle centers 8.5 The excenters and the excircles The internal bisector of each angle and theexternalbisect ...
8.5 The excenters and the excircles 237 Exercise 1.Given a triangleABC, construct a triangle whose sides have the same lengths a ...
Chapter 9 The area of a triangle 1 Heron’s formula for the area of a triangle 2 Heron triangles 3 Heron triangles with consecuti ...
302 The area of a triangle 9.1 Heron’s formula for the area of a triangle Theorem 9.1.The area of a triangle of sidelengthsa,b,c ...
9.2 Heron triangles 303 9.2 Heron triangles A Heron triangle is one whose sidelengths and area are both integers. It can be cons ...
304 The area of a triangle 9.3 Heron triangles with consecutive sides If(b− 1 ,b,b+1, )is a Heron triangle, thenbmust be an even ...
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