File:A source book of problems for geometry, based upon industrial design and architectural ornament (1912) (14578030018).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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onfined to cut glass. Almost every piece containsone or more. The f star is the one used in the UnitedStates flag. 147. History. — Star polygons occur in all periods ofhistoric ornament. Their use dates back to the ancient 1 S. Gunther, pp. 1-92. 132 MISCELLANEOUS INDUSTRIES Greeks when the f star was a symbol of recognitionamong the Pythagoreans.^ Near Winchester, England,are the remains of an old Roman pavement, the designof which includes the ^ star.^ In the church of SanGiovanni e Paulo at Rome is a Byzantine mosaic whichcontains the eight-pointed ^g star.^ Among the mosaicsat St. Marks, Venice, is one that contains the ^ starwithin the five-pointed -^ star.* On the ceiling of oneof the halls in the Alhambra is the ; star within theI star.* Stars of various kinds are found in medievaltiled pavements in western Europe ^ and in medievalembroideries.^ They are extremely common in Saracenicart.* They occur in the ornamentation of primitive peo-ples, especially in symbols of the sun.
Text Appearing After Image:
Fig. 119, 1 Ball, p. 21. 2 Morgan, p. 221. » Wyatt, PI. 5. * Ongania, Folio PI. 30. Calvert, (1), p. 124. « Shaw, (1), PI. XXI. Shaw, (2). 8 Prisse dAvennes, Pis. XC, XCI, XCII. 9 Beauchamp, Pis. 1-^. w Waring, (2), pp. 62 and 63. DESIGNS BASED ON REGULAR POLYGONS 133 EXERCISES148. 1. Construct the five-pointed star shown in Fig. 119. 2. What axes of symmetry has this figure ? 3. Prove that (a) AC= CE = EB, etc. (b) AX =XB = BY, etc. (c) AAUC ^ABVD ^ A CXE, etc. (d) ^BAX = \/.EAB. 4. Prove that points F, 0, C are collinear. Suggestion. — Prove that each point lies on the perpendicular bisec-tor of ^E. 5. Prove that 4 C is divided into mean and extreme ratio at Y andthat ^ F is divided into mean and extreme ratio at X. 6. Prove that Z YXB = 2^ YBX. 7. Prove that XYZUV \s a regular pentagon. 10

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