File:A source book of problems for geometry, based upon industrial design and architectural ornament (1912) (14577998409).jpg

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Identifier: cu31924031218187 (find matches)
Title: A source book of problems for geometry, based upon industrial design and architectural ornament
Year: 1912 (1910s)
Authors: Sykes, Mabel, 1868- Slaught, H. E. (Herbert Ellsworth), 1861-1937 Lennes, N. J. (Nels Johann), 1874-
Subjects: Geometry Decoration and ornament
Publisher: Boston, Allyn and Bacon
Contributing Library: Cornell University Library
Digitizing Sponsor: MSN

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A X B Fig. 84. — From a Roman Mosaic Pavement. Zahn (2), Vol. II, PI. 79, Vol. Ill, PI. 6. 96 MISCELLANEOUS INDUSTRIES EXERCISES105. 1. Give the construction for the figure within the squareABCD in Fig. 84. Suggestion. — First inscribe the circle in the square. 2. Prove that GPYZ is a rhombus. 3. If OP = r, find the length of HK. Ans. r (2 - V2). 4. Also find the areas of ZYPG and EFGHK etc. Ans. (1) ^(3v/2 - 4) ; (2) i:i\\^ - 1). PART 3. DESIGNS FORMED FROM ARCS OF CIRCLES 106. Occurrence. — The figures in this section are foundin all lines of modern industrial design from all-over laceto iron grills and stamped steel ceilings. In the history ofornament they occur in ancient Assyrian ^ and Egyptian 2,in Chinese and Japanese, in Roman and medieval, andin modern art. FIGURES FORMED OF SEMICIRCLES AND QUADRANTS
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A BE F Fig, 85— Design for Iron Grills and Mosaics, EXERCISES107. I. Show how Fig. 85 is constructed from a network ofsquares. 1 Ward (1), Vol. I, p. 126. 2 Ward (2), p. 34 ; Glazier, p. 4. 3 Clifford, pp. 27-35; Jones (2), PI. LIX. DESIGNS FORMED FROM ARCS OF CIRCLES 97 2. Prove that the curved figures CEDHC and CHKLC are con-gruent. Suggestion. — Draw the chords CE, DE, etc., and CH, IIK, etc.Prove that (1) the quadrilaterals thus formed are congruent; (2)corresponding arcs as CE and CH, ED and CH are equal; (3) con-e-sponding arcs lie on the same side of corresponding chords. 3. If ^B = 4, find the perimeter and area of the curved figureCEDHC. 4. If j4B = a, find the perimeter and area of the curved figureCEDHC. Ans. (1) 27ra; (2) 2a\

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