POLYNESIA 



4746 



POLYTHEISM 



It is seen in Fig. 1 that tho sum of the ex- 

 terior angle at b and the interior angle at b is 

 180. Then the sum of the ffcterior and in- 

 terior angles at all the vertices is n, the num- 

 ber of vertices, times 180. But we know that 

 the interior angles equal (n-2)Xl80, and 

 we see that the sum of the exterior angles 

 equals nXl80-(n-2)Xl80, or (n-n+2)X 

 180, or 2X180, or 360, or four right angles. 



A regular polygon may be divided into equal 

 triangles. The area of each triangle is the 

 product of its base and half its altitude. In 



Fig. 1, the area of triangle e o d equals 6 '*- 



The area of the polygon is equal to the num- 

 ber oj sides times the area of each triangle. 

 Let n be number of sides of a regular polygon, 

 1 equal length of each side, and a be the per- 

 pendicular distance from the center to each 



; then area of polygon=nXlX , or area 



of polygon=perimeterX TJ. A - H - 



POLYNESIA, poline'shia, a term applied 

 collectively by modern geographers to a group 

 of Pacific islands lying east of the ISOt/h merid- 

 ian. Polynesia is one of the four divisions of 

 the geographic section of the globe known as 

 Oceania. It includes the Samoan (or Naviga- 

 tor), Tonga (or Friendly), Phoenix, Cook, So- 

 ciety, Marquesas and the Hawaiian islands and 

 a few less important groups. See colored map, 

 with article OCEANIA, for detailed outline of 

 these ocean groups. 



POLYP, pol'ip, a tiny water animal gener- 

 ally found growing in large colonies attached to 

 stones or bits of wood lying on the bottom of 

 streams or in the sea. It is very simple in 

 structure, being a trifle more complex than the 



POLYPS 



sponge; it has little, waving tentacles which 

 reach out to gather its food, while small cells 

 within the body digest it. The colonies of 

 polyps increase in size very rapidly, for the 



young shoot out as buds from the parent and 

 remain attached, so that in time the group 

 looks like a tree. Most of these animals pro- 

 duce bell-shaped structures called medusae, 

 which are soft, gelatinlike bodies that soon 

 separate from the polyps and swim around in 

 the water, being then known as jellyfish. One 

 important member of the family, the hydra, 

 does not live in colonies, but is found in fresh- 

 water streams and pools attached to a stone 

 or weed. It is very small and looks like a tiny 

 white or green spot, but it can move from place 

 to place, feeding itself upon very small water 

 life (see HYDRA, FRESH-WATER). Coral, an- 

 other form of polyp, is described on page 1576. 



POLYPHEMUS, polife'mus, in the Greek 

 myth, a son of Neptune, a Cyclops, who lived 

 with the other Cyclopes on the island of Sicily. 

 All day he wandered about with his flocks, 

 which at night he drove into a huge cave where 

 he lived alone. Ulysses and his companions 

 were cast ashore on the island during their 

 voyaging, and were captured by the giant and 

 shut up in his cave to be devoured. Four were 

 eaten, and then Ulysses with his remaining 

 comrades, having made the giant drunk, 

 blinded him by plunging a heated stick into his 

 one great eye. Roaring with pain, Polyphemus 

 called the other Cyclopes, who asked who was 

 making him suffer. "No Man is hurting me," 

 cried Polyphemus. Now the Cyclopes could 

 not know that No Man was the name by which 

 Ulysses had called himself, so they refused 

 their help, declaring that the pain must be from 

 the gods, in punishment for sin. Mad with 

 rage and pain, Polyphemus stationed himself at 

 the entrance of the cave that no one might 

 escape, but Ulysses and his companions, by 

 tying sheep together in threes and concealing 

 themselves beneath them, passed out in safety. 



POLYTECHNIC , politek' nik, SCHOOLS . 

 See SCHOOL, subhead Technical Schools; MAN- 

 UAL TRAINING. 



POLYTHEISM, pol'itheiz'm, a Greek word 

 meaning belonging to many gods, is the distri- 

 bution of a faith and worship among several 

 gods, as opposed to monotheism, which is the 

 belief in and worship of one God. The general 

 supposition is that monotheism is the original 

 form of worship and that polytheism and other 

 forms of belief sprang from those who aban- 

 doned the first principles. The feeling of 'de- 

 pendence and the inclination to worship are 

 natural to man, hence people living under 

 primitive conditions are easily induced to wor- 

 ship familiar objects or forces that inspire ad- 



