File:A source book of problems for geometry, based upon industrial design and architectural ornament (1912) (14764725025).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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213. The dotted lines in Fig. 176show ABC etc., a regular hexagon,inscribed in a circle, with alternate ver-tices joined as indicated. Fig. 176 —From Pompeian Mosaic. Zahn(21, Vol. Ill, PI. 16. Also Vaulting Plan. Handbuch der Architektur, II, 4, 2, p.71, PL, opposite p. 136, EXERCISES 1. Prove that ^ANG, NOG, GHB, etc., are congruent and equi-lateral. 2. Show how to construct the entire figure. 3. ltAO = r, find the length of GO. 4. If ^ 0 = r-, find the area of (a) The oval GO. (b) The figure GXOYHB. (c) The entire figure A GBHC etc. Ans. - V3. Ans.-Vs.6 Ans. (rf) The cusped figure bounded by the arcs A G, GB, and AB. Ans. — •18 5. What fraction of the hexagon GHKL etc. is occupied by theovals GO, HO, etc. ? 196 GOTHIC TBACERY: FORMS IJV CIRCLESV
Text Appearing After Image:
Fig. 177. — From an old Gothic Wood-carving. Brochure Series, July, 1900, p. 109. EXERCISES 214. 1. Given the circle with the radius .40; construct Fig. 177.Suggestion. — Use Fig. 176. Points A, B, C, etc. are the centers of NG, GH, HK, etc. 2. Construct the inner circle XYZ etc. tangent to the arcs NG,GH, HK, etc. Why is this possible ? 3. If AB = r, find the area of (1) the curved triangle AGN;(2) the cusped hexagon GHK etc.; (3) the circle with radius OX. ^,.(1) ^(t- V3); (2) i(3V3-,r); (3) ;^r^(2-V3). MANY-PARTED ROSETTES—TREATED AS TYPES 215. The designs in this group are treated as general-ized types and are rich in possibilities. Four-part formsof the types shown in Figs. 180-182 are very common.One illustration is found in the window of the First Con-gregational Church, Oakland, Cal., which is based onFig. 180. All-over designs made from this unit are com-mon in Saracenic art. A very handsome one is found inthe Hall of the Abencerrages in the Alhambra.^ Win- 1 Brochure S

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