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Architecture and identity: proceedings of the regional

Книга structure and id structure and IdentityКниги Строительство Год издания: 1983 Формат: pdf Издат.:Aga Khan Award for structure Страниц: 104 Размер: 15,9 ISBN: 9971843692 Язык: Английский0 (голосов: zero) Оценка:-

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Extra info for Architecture and identity: proceedings of the regional seminar in the series Exploring architecture in Islamic cultures

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Problem 2. An isosceles triangle ABC is given with base AB and equal sides AC and BC. Show that the angle at A is equal to the angle at B. 48b so that CD = CE and show that the triangles CAE and CBD are congruent. ] Problem 2 is the fifth proposition in Book I of Euclid’s Elements. 48b) resembles a bridge. The more common explanation is that the fifth proposition in Book I of the Elements is the first real test of the intelligence of the reader and serves as a bridge to the harder propositions that follow.

Problem 4. Consider a triangle inscribed in a circle in such a way that one of its sides is a diameter of the circle. 49 to show that the triangle is a right triangle. α (b) E 44 Chapter 2 ii. Place a square inside R so that one side of the square coincides with one of the shorter sides of the rectangle. Let R 2 be the rectangle that remains. What are the lengths of the sides of R 2? Show that if the rectangle R is golden, then R 2 is golden.

A basic property of isosceles triangles tells us that b = 54°. So 2b = 108°. Now complete the pentagon to the five-­pointed star. 11b and label the points A, B, C, and D as indicated. Notice that the angle CAB = 72°. Now comes the hard part. This is to show that the rectangle obtained by constructing a square over DA and extending it by using the segment AB is golden! 2 describes in detail how Euclid does this in his Elements. The rest is easy. 11b are obtained in the same way. 10 is indeed equal to 72°.

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