2182:
2092:
213:
779:
2968:
40:
1743:
2523:
2247:. The major axis of the prolate spheroid does not run through the satellite's poles in this case, but through the two points on its equator directly facing toward and away from the primary. This combines with the smaller oblate distortion from the synchronous rotation to cause the body to become triaxial.
2028:
All modern geodetic ellipsoids are defined by the semi-major axis plus either the semi-minor axis (giving the aspect ratio), the flattening, or the first eccentricity. While these definitions are mathematically interchangeable, real-world calculations must lose some precision. To avoid confusion, an
551:
961:
1303:
196:
originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape; that is how the term is used in some older papers on geodesy (for example, referring to truncated spherical harmonic expansions of the
1516:
1531:
2335:
2023:
774:{\displaystyle S_{\text{oblate}}=2\pi a^{2}\left(1+{\frac {1-e^{2}}{e}}\operatorname {arctanh} e\right)=2\pi a^{2}+\pi {\frac {c^{2}}{e}}\ln \left({\frac {1+e}{1-e}}\right)\qquad {\mbox{where}}\quad e^{2}=1-{\frac {c^{2}}{a^{2}}}.}
354:
827:
467:
1010:
and can no longer directly be identified with the eccentricity. Both of these results may be cast into many other forms using standard mathematical identities and relations between parameters of the ellipse.
2262:, used to analyze wave propagation and interference in space, are a series of concentric prolate spheroids with principal axes aligned along the direct line-of-sight between a transmitter and a receiver.
1177:
1087:
1919:
1850:
2340:
1935:
1199:
2590:
1387:
1738:{\displaystyle H(\beta ,\lambda )={\frac {c\left(2a^{2}+\left(c^{2}-a^{2}\right)\cos ^{2}\beta \right)}{2a\left(a^{2}+\left(c^{2}-a^{2}\right)\cos ^{2}\beta \right)^{\frac {3}{2}}}}.}
2518:{\displaystyle {\begin{aligned}A=B&={\tfrac {1}{5}}M\left(a^{2}+c^{2}\right),\\C&={\tfrac {1}{5}}M\left(a^{2}+b^{2}\right)={\tfrac {2}{5}}M\left(a^{2}\right),\end{aligned}}}
1930:
258:
2986:
956:{\displaystyle S_{\text{prolate}}=2\pi a^{2}\left(1+{\frac {c}{ae}}\arcsin \,e\right)\qquad {\mbox{where}}\quad e^{2}=1-{\frac {a^{2}}{c^{2}}}.}
383:
2235:
In contrast to being distorted into oblate spheroids via rapid rotation, celestial objects distort slightly into prolate spheroids via
2893:
2676:
1118:
1025:
2807:
2631:
2662:
1298:{\displaystyle {\boldsymbol {\sigma }}(\beta ,\lambda )=(a\cos \beta \cos \lambda ,a\cos \beta \sin \lambda ,c\sin \beta ),}
2621:
1867:
1792:
2282:
2538:
1856:
1511:{\displaystyle K(\beta ,\lambda )={\frac {c^{2}}{\left(a^{2}+\left(c^{2}-a^{2}\right)\cos ^{2}\beta \right)^{2}}},}
983:
801:
2329:. However, in a spheroid the minor axes are symmetrical. Therefore, our inertial terms along the major axes are:
2045:, prolate, and oblate spheroidal, where the polar axis is assumed to be the spin axis (or direction of the spin
117:
2306:
is that of an ellipsoid with an additional axis of symmetry. Given a description of a spheroid as having a
2243:, which becomes slightly more or less prolate in its orbit due to a slight eccentricity, causing intense
2050:
178:
150:
80:
76:
2972:
2909:
2835:
2146:
2136:
2862:
2914:
2641:
2170:
2112:
2061:
2018:{\displaystyle {\begin{aligned}e&={\sqrt {2f-f^{2}}}\\f&=1-{\sqrt {1-e^{2}}}\end{aligned}}}
1318:
1188:
174:
154:
2738:
2776:
2768:
2205:
2158:
2072:
1378:
201:
198:
1861:(usually simply eccentricity, as above) is often used instead of flattening. It is defined by:
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3004:
2889:
2879:
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2672:
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2303:
2181:
2166:
2080:
2058:
186:
96:
1748:
Both of these curvatures are always positive, so that every point on a spheroid is elliptic.
120:
is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its
2843:
2823:
2760:
2636:
2606:
2601:
2239:
when they orbit a massive body in a close orbit. The most extreme example is
Jupiter's moon
2217:
2193:
The prolate spheroid is the approximate shape of the ball in several sports, such as in the
2140:
2076:
2046:
1007:
480:
is the distance from centre to pole along the symmetry axis. There are two possible cases:
2068:
2054:
1002:
can be used to calculate the surface area of a prolate spheroid and vice versa. However,
2980:
2839:
2091:
2796:
2266:
2229:
2038:
1522:
349:{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}+{\frac {z^{2}}{c^{2}}}=1.}
2998:
2780:
2611:
2277:
elements are shaped like prolate spheroids. In anatomy, near-spheroid organs such as
2221:
2204:
of the Solar System approximate prolate spheroids in shape, though they are actually
364:
92:
2716:
2693:
2259:
2213:
2150:
2128:
1786:, is the ratio of the equatorial-polar length difference to the equatorial length:
1758:
543:
181:
model uses a spheroid whose radius is 6,378.137 km (3,963.191 mi) at the
2037:
The most common shapes for the density distribution of protons and neutrons in an
2029:
ellipsoidal definition considers its own values to be exact in the form it gives.
2751:
Greenburg, John L. (1995). "Isaac Newton and the
Problem of the Earth's Shape".
2255:
2154:
166:
135:
212:
2307:
2274:
2194:
2186:
2132:
2100:
2049:
vector). Deformed nuclear shapes occur as a result of the competition between
1774:
162:
121:
113:
103:
2938:
2297:
2244:
2240:
2042:
1327:
88:
240:
The equation of a tri-axial ellipsoid centred at the origin with semi-axes
2967:
2288:
Many submarines have a shape which can be described as prolate spheroid.
2278:
2270:
17:
2772:
2764:
2616:
2120:
2096:
987:
805:
182:
170:
146:
84:
73:
462:{\displaystyle {\frac {x^{2}+y^{2}}{a^{2}}}+{\frac {z^{2}}{c^{2}}}=1.}
39:
2251:
2225:
2209:
2124:
2116:
2108:
158:
139:
131:
173:
the Earth is often approximated by an oblate spheroid, known as the
2848:
2201:
2180:
2162:
2090:
2739:
Introduction à la Géodésie et au geopositionnement par satellites
2169:. Earth's diverse cartographic and geodetic systems are based on
2626:
2236:
2161:'s theories for their interpretation, reasoned that Jupiter and
2979:
2826:(October 1973), "The Distance to the Crab Nebula and NP 0532",
993:
These formulas are identical in the sense that the formula for
2910:"What Do a Submarine, a Rocket and a Football Have in Common?"
165:
in the direction of its axis of rotation. For that reason, in
1772:, is the ratio of the polar to equatorial lengths, while the
1172:{\displaystyle {\tfrac {\pi }{6}}A^{2}C\approx 0.523A^{2}C.}
1082:{\displaystyle {\tfrac {4}{3}}\pi a^{2}c\approx 4.19a^{2}c.}
216:
The assignment of semi-axes on a spheroid. It is oblate if
2107:
The oblate spheroid is the approximate shape of rotating
138:. If the generating ellipse is a circle, the result is a
2317:, the moments of inertia along these principal axes are
966:
The prolate spheroid is generated by rotation about the
2828:
1924:
The relations between eccentricity and flattening are:
784:
The oblate spheroid is generated by rotation about the
2549:
2476:
2425:
2360:
1123:
1030:
900:
718:
31:
2541:
2338:
1933:
1870:
1795:
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1390:
1202:
1121:
1028:
830:
554:
386:
261:
2250:
The term is also used to describe the shape of some
1914:{\displaystyle e={\sqrt {1-{\frac {c^{2}}{a^{2}}}}}}
1845:{\displaystyle f={\frac {a-c}{a}}=1-{\frac {c}{a}}.}
87:
about one of its principal axes; in other words, an
2795:
2584:
2517:
2017:
1913:
1844:
1737:
1510:
1297:
1171:
1081:
955:
773:
461:
348:
2585:{\displaystyle M={\tfrac {4}{3}}\pi a^{2}c\rho .}
185:and 6,356.752 km (3,949.903 mi) at the
161:) is not quite a sphere, but instead is slightly
2798:The Story of Civilization: The Age of Louis XIV
1019:The volume inside a spheroid (of any kind) is
476:is the equatorial radius of the spheroid, and
2083:is also a shape of archaeological artifacts.
2071:. Rotating equilibrium spheroids include the
1189:Radius of the Earth § Radii of curvature
8:
2794:Durant, Will; Durant, Ariel (28 July 1997).
2714:A derivation of this result may be found at
2691:A derivation of this result may be found at
2717:"Prolate Spheroid - from Wolfram MathWorld"
2302:For a spheroid having uniform density, the
2694:"Oblate Spheroid - from Wolfram MathWorld"
2127:. Saturn is the most oblate planet in the
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970:-axis of an ellipse with semi-major axis
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835:
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788:-axis of an ellipse with semi-major axis
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262:
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2888:(6 ed.). Elsevier Health Sciences.
2886:Introduction to Vascular Ultrasonography
211:
33:Spheroids with vertical rotational axes
2884:John Pellerito, Joseph F Polak (2012).
2719:. Mathworld.wolfram.com. 7 October 2003
2653:
1204:
2298:Ellipsoid § Dynamical properties
1112:is the polar diameter, the volume is
252:aligned along the coordinate axes is
46:
27:Surface formed by rotating an ellipse
7:
2165:are oblate spheroids owing to their
102:If the ellipse is rotated about its
2532:is the mass of the body defined as
2099:is a slight oblate spheroid with a
1193:Let a spheroid be parameterized as
177:, instead of a sphere. The current
2863:"Nuclear fission - Fission theory"
25:
2943:MathWorld--A Wolfram Web Resource
2966:
2123:, and the quickly spinning star
1102:is the equatorial diameter, and
359:The equation of a spheroid with
38:
1762:of an oblate spheroid/ellipse,
982:may again be identified as the
906:
898:
724:
716:
145:Due to the combined effects of
2632:Prolate spheroidal coordinates
1550:
1538:
1406:
1394:
1289:
1226:
1220:
1208:
1:
2622:Oblate spheroidal coordinates
2737:Brial P., Shaalan C.(2009),
2157:'s pendulum experiments and
2173:, all of which are oblate.
2053:repulsion between protons,
2033:Occurrence and applications
3026:
2295:
1186:
2753:History of Exact Sciences
2281:may be measured by their
800:may be identified as the
37:
2824:Trimble, Virginia Louise
2759:(4). Springer: 371–391.
2661:Torge, Wolfgang (2001).
2067:Spheroids are common in
811:A prolate spheroid with
532:An oblate spheroid with
2987:Encyclopædia Britannica
2867:Encyclopedia Britannica
2696:. Mathworld.wolfram.com
1377:. Then, the spheroid's
66:ellipsoid of revolution
2990:(11th ed.). 1911.
2586:
2519:
2190:
2104:
2019:
1915:
1846:
1739:
1512:
1299:
1173:
1083:
957:
775:
463:
350:
237:
226:(left) and prolate if
2587:
2520:
2184:
2094:
2020:
1916:
1847:
1740:
1513:
1300:
1174:
1084:
958:
776:
519:reduces to a sphere.
464:
351:
215:
179:World Geodetic System
2975:at Wikimedia Commons
2539:
2336:
2292:Dynamical properties
2171:reference ellipsoids
2137:planetary flattening
1931:
1868:
1793:
1532:
1388:
1200:
1119:
1026:
974:and semi-minor axis
828:
792:and semi-minor axis
552:
384:
367:is given by setting
259:
70:rotational ellipsoid
2937:Weisstein, Eric W.
2915:Scientific American
2840:1973PASP...85..579T
2642:Translation of axes
2283:long and short axes
2206:triaxial ellipsoids
2115:, including Earth,
1319:parametric latitude
175:reference ellipsoid
155:figure of the Earth
130:, flattened like a
124:, the result is an
112:, elongated like a
64:, also known as an
34:
2765:10.1007/BF00374704
2582:
2558:
2515:
2513:
2485:
2434:
2369:
2191:
2159:Christiaan Huygens
2105:
2073:Maclaurin spheroid
2015:
2013:
1911:
1842:
1735:
1508:
1379:Gaussian curvature
1295:
1169:
1132:
1079:
1039:
953:
904:
771:
722:
505:: prolate spheroid
459:
346:
238:
202:geopotential model
106:, the result is a
32:
2971:Media related to
2918:. 8 November 2010
2669:Walter de Gruyter
2557:
2484:
2433:
2368:
2313:, and minor axes
2304:moment of inertia
2177:Prolate spheroids
2167:centrifugal force
2009:
1969:
1909:
1907:
1837:
1818:
1730:
1726:
1503:
1131:
1038:
948:
903:
884:
838:
821:has surface area
766:
721:
710:
674:
618:
562:
493:: oblate spheroid
451:
424:
338:
311:
284:
118:American football
97:circular symmetry
95:. A spheroid has
58:
57:
16:(Redirected from
3017:
2991:
2983:
2981:"Spheroid"
2970:
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2953:
2951:
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2728:
2726:
2724:
2712:
2706:
2705:
2703:
2701:
2689:
2683:
2682:
2667:(3rd ed.).
2658:
2637:Rotation of axes
2607:Equatorial bulge
2602:Ellipsoidal dome
2591:
2589:
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2583:
2572:
2571:
2559:
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2388:
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2328:
2324:
2320:
2316:
2312:
2141:equatorial bulge
2135:of 0.09796. See
2113:celestial bodies
2087:Oblate spheroids
2077:Jacobi ellipsoid
2069:3D cell cultures
2047:angular momentum
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2022:
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1314:reduced latitude
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109:prolate spheroid
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2671:. p. 104.
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2318:
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2300:
2294:
2208:. Examples are
2179:
2153:, working from
2089:
2055:surface tension
2051:electromagnetic
2035:
2012:
2011:
1999:
1978:
1972:
1971:
1959:
1941:
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199:Earth's gravity
127:oblate spheroid
91:with two equal
28:
23:
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5:
3023:
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3013:
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2962:
2961:External links
2959:
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2849:10.1086/129507
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2212:'s satellites
2178:
2175:
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2039:atomic nucleus
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2006:
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1523:mean curvature
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472:The semi-axis
470:
469:
458:
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448:
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209:
206:
93:semi-diameters
56:
55:
50:
44:
43:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
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2974:
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2964:
2960:
2944:
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2930:
2917:
2916:
2911:
2905:
2902:
2897:
2895:9781455737666
2891:
2887:
2881:
2876:
2873:
2868:
2864:
2858:
2855:
2850:
2845:
2841:
2837:
2833:
2829:
2825:
2819:
2816:
2811:
2805:
2802:. MJF Books.
2800:
2799:
2790:
2787:
2782:
2778:
2774:
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2766:
2762:
2758:
2754:
2747:
2744:
2740:
2734:
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2718:
2711:
2708:
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2685:
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2678:9783110170726
2674:
2670:
2666:
2665:
2657:
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2647:
2643:
2640:
2638:
2635:
2633:
2630:
2628:
2625:
2623:
2620:
2618:
2615:
2613:
2612:Great ellipse
2610:
2608:
2605:
2603:
2600:
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2595:
2579:
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2267:atomic nuclei
2263:
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2260:Fresnel zones
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2176:
2174:
2172:
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2160:
2156:
2152:
2148:
2147:Enlightenment
2144:
2143:for details.
2142:
2138:
2134:
2130:
2126:
2122:
2118:
2114:
2110:
2102:
2098:
2093:
2086:
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2070:
2065:
2063:
2062:shell effects
2060:
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2040:
2032:
2030:
2004:
2000:
1996:
1993:
1988:
1985:
1982:
1980:
1975:
1964:
1960:
1956:
1953:
1950:
1945:
1943:
1938:
1927:
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1778:(also called
1777:
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1100:
1096:
1076:
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1060:
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1054:
1049:
1045:
1041:
1035:
1032:
1022:
1021:
1020:
1014:
1012:
1009:
1006:then becomes
997:
991:
989:
985:
978:; therefore,
950:
943:
939:
933:
929:
923:
920:
917:
912:
908:
894:
890:
886:
880:
877:
873:
868:
865:
861:
855:
851:
847:
844:
841:
832:
824:
823:
822:
819:
815:
809:
807:
803:
768:
761:
757:
751:
747:
741:
738:
735:
730:
726:
712:
706:
703:
700:
695:
692:
689:
683:
679:
676:
671:
666:
662:
656:
653:
648:
644:
640:
637:
634:
630:
626:
623:
620:
615:
609:
605:
601:
598:
592:
589:
585:
579:
575:
571:
568:
565:
556:
548:
547:
546:
545:
540:
536:
527:
522:
520:
517:
513:
503:
499:
495:
491:
487:
483:
482:
481:
456:
453:
446:
442:
436:
432:
426:
419:
415:
408:
404:
400:
395:
391:
380:
379:
378:
375:
371:
366:
365:symmetry axis
343:
340:
333:
329:
323:
319:
313:
306:
302:
296:
292:
286:
279:
275:
269:
265:
255:
254:
253:
234:
230:
224:
220:
214:
207:
205:
203:
200:
195:
190:
188:
184:
180:
176:
172:
168:
164:
160:
156:
152:
148:
143:
141:
137:
133:
129:
128:
123:
119:
115:
111:
110:
105:
100:
98:
94:
90:
86:
82:
78:
75:
71:
67:
63:
54:
51:
49:
45:
41:
36:
30:
19:
2985:
2946:. Retrieved
2942:
2932:
2920:. Retrieved
2913:
2904:
2885:
2875:
2866:
2857:
2834:(507): 579,
2831:
2827:
2818:
2797:
2789:
2756:
2752:
2746:
2733:
2721:. Retrieved
2710:
2698:. Retrieved
2687:
2663:
2656:
2527:
2301:
2287:
2264:
2254:such as the
2249:
2237:tidal forces
2234:
2228:' satellite
2199:
2192:
2151:Isaac Newton
2145:
2129:Solar System
2106:
2066:
2036:
2027:
1923:
1858:eccentricity
1857:
1854:
1779:
1773:
1768:
1764:
1759:aspect ratio
1757:
1755:
1752:Aspect ratio
1747:
1520:
1372:
1349:
1317:
1313:
1307:
1192:
1108:
1104:
1098:
1094:
1091:
1018:
995:
992:
984:eccentricity
965:
817:
813:
810:
802:eccentricity
796:, therefore
783:
544:surface area
538:
534:
531:
515:
511:
509:The case of
508:
501:
497:
489:
485:
471:
373:
369:
358:
239:
232:
228:
222:
218:
193:
191:
157:(and of all
144:
126:
125:
108:
107:
101:
79:obtained by
69:
65:
61:
59:
52:
47:
29:
2256:Crab Nebula
2155:Jean Richer
2095:The planet
167:cartography
134:or a plain
2999:Categories
2939:"Spheroid"
2809:1567310192
2648:References
2308:major axis
2296:See also:
2275:lanthanide
2195:rugby ball
2187:rugby ball
2149:scientist
2133:flattening
2111:and other
2103:of 0.06487
2101:flattening
1855:The first
1780:oblateness
1775:flattening
1187:See also:
523:Properties
122:minor axis
114:rugby ball
104:major axis
2973:Spheroids
2781:121268606
2577:ρ
2561:π
2245:volcanism
2218:Enceladus
2131:, with a
2043:spherical
1997:−
1989:−
1957:−
1883:−
1827:−
1809:−
1711:β
1708:
1680:−
1630:β
1627:
1599:−
1548:λ
1542:β
1490:β
1487:
1459:−
1404:λ
1398:β
1328:longitude
1287:β
1284:
1272:λ
1269:
1263:β
1260:
1248:λ
1245:
1239:β
1236:
1218:λ
1212:β
1205:σ
1183:Curvature
1148:≈
1126:π
1058:≈
1042:π
1008:imaginary
924:−
848:π
742:−
704:−
680:
657:π
641:π
624:
602:−
572:π
192:The word
163:flattened
89:ellipsoid
18:Spheroids
3010:Quadrics
3005:Surfaces
2880:Page 559
2773:41134011
2596:See also
2271:actinide
2200:Several
2081:Spheroid
2075:and the
1767: :
1521:and its
1371:−π <
236:(right).
208:Equation
194:spheroid
151:rotation
81:rotating
62:spheroid
2922:13 June
2836:Bibcode
2723:24 June
2700:24 June
2664:Geodesy
2617:Lentoid
2269:of the
2252:nebulae
2230:Miranda
2121:Jupiter
2109:planets
2097:Jupiter
2059:quantum
1375:< +π
1366:
1354:
1346:
1334:
1326:is the
1312:is the
988:ellipse
986:. (See
837:prolate
806:ellipse
804:. (See
621:arctanh
363:as the
183:Equator
171:geodesy
159:planets
147:gravity
136:M&M
85:ellipse
77:surface
74:quadric
72:, is a
53:prolate
2948:16 May
2892:
2806:
2779:
2771:
2675:
2528:where
2325:, and
2279:testis
2226:Uranus
2222:Tethys
2220:, and
2210:Saturn
2125:Altair
2117:Saturn
1352:< +
1330:, and
1308:where
1015:Volume
999:oblate
887:arcsin
561:oblate
153:, the
140:sphere
132:lentil
116:. The
48:oblate
2777:S2CID
2769:JSTOR
2741:, p.8
2627:Ovoid
2315:a = b
2214:Mimas
2202:moons
2163:Earth
1348:<
1151:0.523
902:where
816:>
720:where
537:<
500:>
488:<
231:>
221:<
187:poles
2950:2018
2924:2015
2890:ISBN
2882:in:
2804:ISBN
2725:2014
2702:2014
2673:ISBN
2273:and
2265:The
2224:and
2139:and
2057:and
2041:are
1756:The
1369:and
1061:4.19
990:.)
542:has
528:Area
248:and
169:and
149:and
2844:doi
2761:doi
1699:cos
1618:cos
1525:is
1478:cos
1381:is
1316:or
1281:sin
1266:sin
1257:cos
1242:cos
1233:cos
1107:= 2
1097:= 2
1092:If
808:.)
204:).
83:an
68:or
3001::
2984:.
2941:.
2912:.
2865:.
2842:,
2832:85
2830:,
2775:.
2767:.
2757:49
2755:.
2321:,
2285:.
2258:.
2241:Io
2232:.
2216:,
2197:.
2185:A
2119:,
2079:.
2064:.
1782:)
1322:,
677:ln
514:=
457:1.
377::
372:=
344:1.
244:,
189:.
142:.
99:.
60:A
2952:.
2926:.
2898:.
2869:.
2846::
2838::
2812:.
2783:.
2763::
2727:.
2704:.
2681:.
2580:.
2574:c
2569:2
2565:a
2555:3
2552:4
2546:=
2543:M
2530:M
2509:,
2505:)
2500:2
2496:a
2492:(
2488:M
2482:5
2479:2
2473:=
2469:)
2463:2
2459:b
2455:+
2450:2
2446:a
2441:(
2437:M
2431:5
2428:1
2422:=
2415:C
2408:,
2404:)
2398:2
2394:c
2390:+
2385:2
2381:a
2376:(
2372:M
2366:5
2363:1
2357:=
2350:B
2347:=
2344:A
2327:B
2323:A
2319:C
2311:c
2189:.
2005:2
2001:e
1994:1
1986:1
1983:=
1976:f
1965:2
1961:f
1954:f
1951:2
1946:=
1939:e
1903:2
1899:a
1893:2
1889:c
1880:1
1875:=
1872:e
1840:.
1835:a
1832:c
1824:1
1821:=
1816:a
1812:c
1806:a
1800:=
1797:f
1784:f
1769:a
1765:c
1733:.
1724:2
1721:3
1715:)
1703:2
1694:)
1688:2
1684:a
1675:2
1671:c
1666:(
1662:+
1657:2
1653:a
1648:(
1643:a
1640:2
1634:)
1622:2
1613:)
1607:2
1603:a
1594:2
1590:c
1585:(
1581:+
1576:2
1572:a
1568:2
1564:(
1560:c
1554:=
1551:)
1545:,
1539:(
1536:H
1506:,
1499:2
1494:)
1482:2
1473:)
1467:2
1463:a
1454:2
1450:c
1445:(
1441:+
1436:2
1432:a
1427:(
1420:2
1416:c
1410:=
1407:)
1401:,
1395:(
1392:K
1373:λ
1363:2
1360:/
1357:π
1350:β
1343:2
1340:/
1337:π
1332:−
1324:λ
1310:β
1293:,
1290:)
1278:c
1275:,
1254:a
1251:,
1230:a
1227:(
1224:=
1221:)
1215:,
1209:(
1167:.
1164:C
1159:2
1155:A
1145:C
1140:2
1136:A
1129:6
1109:c
1105:C
1099:a
1095:A
1077:.
1074:c
1069:2
1065:a
1055:c
1050:2
1046:a
1036:3
1033:4
1004:e
996:S
980:e
976:a
972:c
968:z
951:.
944:2
940:c
934:2
930:a
921:1
918:=
913:2
909:e
895:)
891:e
881:e
878:a
874:c
869:+
866:1
862:(
856:2
852:a
845:2
842:=
833:S
818:a
814:c
798:e
794:c
790:a
786:z
769:.
762:2
758:a
752:2
748:c
739:1
736:=
731:2
727:e
713:)
707:e
701:1
696:e
693:+
690:1
684:(
672:e
667:2
663:c
654:+
649:2
645:a
638:2
635:=
631:)
627:e
616:e
610:2
606:e
599:1
593:+
590:1
586:(
580:2
576:a
569:2
566:=
557:S
539:a
535:c
516:c
512:a
502:a
498:c
490:a
486:c
478:c
474:a
454:=
447:2
443:c
437:2
433:z
427:+
420:2
416:a
409:2
405:y
401:+
396:2
392:x
374:b
370:a
361:z
341:=
334:2
330:c
324:2
320:z
314:+
307:2
303:b
297:2
293:y
287:+
280:2
276:a
270:2
266:x
250:c
246:b
242:a
233:a
229:c
223:a
219:c
20:)
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