File:A source book of problems for geometry, based upon industrial design and architectural ornament (1912) (14762309884).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

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he ^ star, how many regular polygons of 16sides occur? See Fig. 121c. DESIGNS BASED ON STAR-POLYGONS 153. Fig. 124 is the only one of the following designswhich is from a modern source. The rest are Mohamme-dan or Arabic. While only extremely simple Moham-medan designs are here given, they are characteristic ofthat style, which is highly original, strikingly geometrical,and totally unlike anything else in history. The factthat the Koran forbade the use of all living forms indecoration and art, undoubtedly accounts for its peculiar DESIGNS BASED ON REGULAR POLYGONS 141 character. The most complicated interlacing geometricalforms abound in endless variety. It is a style of orna-ment especially adapted to surface decoration. It isexecuted in wood, stone, plaster, clay, or mosaic, and com-pletely covers pulpits, domes, vaults, and exterior andinterior walls. Window lattices are of the same design.This style characterizes Mohammedan art to-day and hasstrongly influenced Spanish decoration.
Text Appearing After Image:
EXERCISES154. 1. Construct the design shown in Fig. 124. Suggestion. — ABCD etc. is a regular hexagon with the circle in-scribed. EFGHK etc. is the regular duodecagon. EPGSK etc. is the 6-pointedQR = RS, etc. T^j star. BF = FM, CH = HQ, etc. MN = NP, 142 MISCELLANEOUS INDUSTBIES ^ w ^^\ \ ^^0^ 2. Prove that(a) FB=CH= DL, etc.(ft) MF= HQ = LT,etc. (c) PN= SR= VU, etc. (d) EM = iVG= GQ = QK, etc. (e) EN = NG = GR = -RA:, etc. 3. Prove that(a) Figures EPGN, GSKR, etc. are congruent. (6) Figures ENGM, GRKQ, etc. arecongruent. (e) Figures £M(?F, GHKQ, etc. are p,g ;24«.-Parquet Flooring. congiuent. (rf) Figures EBFG, GHKC, etc. are congruent. 4. Prove that (a) Z iVCii = Z ieA(7, etc.(ft) Z MGQ = /. QKT, etc.(c) Z £iVG = Z GRK, etc. 5. If £0 = r, find length of EP. - ^ns. ^ V2. 6. If EO = r, find the area of (1) A EPG, (2) star EPGSK etc. Am. (1) !^; (2) ^-(VS- 1). 7. If EO = r, find the area of (1) the hexagon ABCD etc.,(2) the figure EPGB. Ans. (1) 2 r^VS; (2) ^(3 + V3). 8. If -BO =

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