File:A source book of problems for geometry, based upon industrial design and architectural ornament (1912) (14578174687).jpg

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

View Book Page: Book Viewer
About This Book: Catalog Entry
View All Images: All Images From Book
Click here to view book online to see this illustration in context in a browseable online version of this book.

Text Appearing Before Image:
Fig. 766. — Mosaic Floor Design. 6. li AB = a and AE = ^—~—^, find the area of the squareAETN, of the rhombus EXZT, and of the entire cross in Fig. 76a.^«s.(l)g(ll-6V2); (2)g(llV2-12); (3) ;;(1) - 6V2). THE TWO-EIGHTHS STAR 97. The I star is formed by joining every second ver-tex of the octagon and is composed of two superposedsquares. When inscribed in a given square, it is relatedto the octagon discussed in § 88. Figures 77 and 83 showit as it most commonly occurs. Fitted together with cer-tain peculiar crosses, as in Fig. 77a, it forms a very commonall-over pattern, which was executed in tiles in Saracenicdecoration.! Figure 78 is an Arabic form. The irregu-lar form suggested in § 99, Ex. 4, is from a Roman mo-saic.^ Figure 83 occurs also in both the Arabic and theRoman, and is extremely common in modern ornament. 1 Furnival PI. 81, Cut. 2 Price. DESIGNS CONTAINING EIGHT-POINTED STABS 87
Text Appearing After Image:
- Parquet Flooring. Fig. 77a.- 98. In Fig. 77 circle O is tangent to the sides of the square ABCD atpoints E, F, G, and H, and intersects the diagonals at points K, L, M, and NPoints E, F, G, and H, also K, L, M, and N are joined. Then the otherpoints are joined as indicated. EXERCISES 1. Prove that (a) EFGH and KLMN are congruent squares; (b) XYZW is asquare; (c) DA, KN, and XW are parallel; (rf) IIR = RN = NS;(e) ROhhsBotsANOH; (/) P/JSrO etc. is a regular octagon. 2. If AB = a, find area of circle that could be inscribed inoctagon PRSTU etc. Ans. ^. 3. If AB = a, find the length of HR and RS. Ans. (I) ^(V2-l); (2) ;(2-V2). 4. If AB = a, find the area of figure OSNR and of the entire star KPHRN etc. Ans. (1) ^(2 - V2); (2) a\^ - V2). 8 5. Compare results in Ex. 4 with those given for Fig. 71a. (See§ 88, Ex. 5.) Notice that the area of star KPHRN etc. (Fig. 77) istwice the area of star WKXL Y etc. in Fig. 71. 88 MISCELLANEOUS INDUSTRIES 6. Find area of figure HRNSGD. Ans.^(V2- 1). 7

Note About Images