MathJaxMap['math_1'] = '1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,…';
MathJaxMap['math_2'] = 'ϕ=1+52≈1.618033';
MathJaxMap['math_3'] = 'l−m=m−w';
MathJaxMap['math_4'] = 'l÷s=s÷w or ls=sw';
MathJaxMap['math_5'] = 'relative price change =old market share of beef×new cost of beefold cost of beef +old market share of chicken×new cost of chickenold cost of chicken =0.5×6.004.00+0.5×2.002.00 =0.75+0.50=1.25';
MathJaxMap['math_6'] = 'relative price change=(new cost of beefold cost of beef)(old market share of beef)×(new cost of chickenold cost of chicken)(old market share of chicken)=(6.004.00)0.5×(2.002.00)0.5=1.50×1.00≈1.225';
MathJaxMap['math_7'] = 'ls=sw=x';
MathJaxMap['math_8'] = 'x=ls=s+ws= ss+ws=1+ws';
MathJaxMap['math_9'] = 'x=1+1x';
MathJaxMap['math_10'] = 'x2=x+1 or x2−x−1=0';
MathJaxMap['math_11'] = 'ax2+bx+c=0';
MathJaxMap['math_12'] = 'x=−b±b2−4ac2a';
MathJaxMap['math_13'] = 'x=1+52≈1.618033 and x=1−52≈−0.618033';
MathJaxMap['math_14'] = '112132538513821131.02.01.51.666…1.61.6251.615…';
MathJaxMap['math_15'] = 'FnFn−1=Fn−1+Fn−2Fn−1=1+Fn−2Fn−1';
MathJaxMap['math_16'] = 'x=1+1x';
MathJaxMap['math_17'] = 'Glide:pppppppppGlide reflection:pbpbpbpbp';
MathJaxMap['math_18'] = '{…, T−3, T−2, T−1, I, T, T2, T3,…}';
MathJaxMap['math_19'] = '{…, G−3, G−2=T−1, G−1, I, G, G2=T, G3,…}=〈G〉';
MathJaxMap['math_20'] = '{…,T−3,T−2,T−1,I,T,T2,T3,…; …,T−3V,T−2V,T−1V,V,TV,T2V,T3V,…}';
MathJaxMap['math_21'] = '〈T,V|VT=T−1V〉';
MathJaxMap['math_22'] = 'ZZZZZZZZZUUUUUUUUU';
MathJaxMap['math_23'] = 'L1=1,L2=3, and Ln+1=Ln+Ln−1 for n≥2';
MathJaxMap['math_24'] = 'L2L1,L3L2,…L10L9';
MathJaxMap['math_25'] = 'Fn=15(1+52)n−15(1−52)n';
MathJaxMap['math_26'] = '21x+1y=2xyx+y';
MathJaxMap['math_27'] = 'G1=1,G2=1, and Gn+1=pGn+qGn−1 for n≥2';
MathJaxMap['math_28'] = 'MOM WOW pod Mud bUM';
MathJaxMap['math_29'] = 'n';
MathJaxMap['math_30'] = 'Fn';
MathJaxMap['math_31'] = 'F1=1, F2=1';
MathJaxMap['math_32'] = 'Fn+1=Fn+Fn−1';
MathJaxMap['math_33'] = 'n≥2';
MathJaxMap['math_34'] = 'F12';
MathJaxMap['math_35'] = 'n';
MathJaxMap['math_36'] = 'n=1';
MathJaxMap['math_37'] = '(ϕ)';
MathJaxMap['math_38'] = 'ϕ';
MathJaxMap['math_39'] = 'ϕ';
MathJaxMap['math_40'] = 'l';
MathJaxMap['math_41'] = 'w';
MathJaxMap['math_42'] = 'm=(l+w)/2';
MathJaxMap['math_43'] = 'm';
MathJaxMap['math_44'] = 'l';
MathJaxMap['math_45'] = 'w';
MathJaxMap['math_46'] = 'n';
MathJaxMap['math_47'] = 'n';
MathJaxMap['math_48'] = 's';
MathJaxMap['math_49'] = 'sw';
MathJaxMap['math_50'] = 'lw=s2';
MathJaxMap['math_51'] = 's';
MathJaxMap['math_52'] = 'l';
MathJaxMap['math_53'] = 'w';
MathJaxMap['math_54'] = 's';
MathJaxMap['math_55'] = 'l';
MathJaxMap['math_56'] = 'w';
MathJaxMap['math_57'] = 'l';
MathJaxMap['math_58'] = 's';
MathJaxMap['math_59'] = 'l';
MathJaxMap['math_60'] = 'w=l−s';
MathJaxMap['math_61'] = 'l';
MathJaxMap['math_62'] = 's=lw';
MathJaxMap['math_63'] = 'l';
MathJaxMap['math_64'] = 'w';
MathJaxMap['math_65'] = 'n';
MathJaxMap['math_66'] = 'n';
MathJaxMap['math_67'] = 'n';
MathJaxMap['math_68'] = 'x1, x2…, xn';
MathJaxMap['math_69'] = 'x1⋅x2⋅⋅⋅⋅⋅xnn';
MathJaxMap['math_70'] = '1⋅2⋅3⋅44=244=241/4≈2.213';
MathJaxMap['math_71'] = '$6/$4=1.5';
MathJaxMap['math_72'] = '$2/$2=1.0';
MathJaxMap['math_73'] = '$50/$40=1.25';
MathJaxMap['math_74'] = '1.50×1.00≈1.225';
MathJaxMap['math_75'] = '$49=1.225×$40';
MathJaxMap['math_76'] = 'l';
MathJaxMap['math_77'] = 'w';
MathJaxMap['math_78'] = 'l=w+s';
MathJaxMap['math_79'] = 'w';
MathJaxMap['math_80'] = 'l';
MathJaxMap['math_81'] = 'ϕ';
MathJaxMap['math_82'] = 'x';
MathJaxMap['math_83'] = 'l=s+w';
MathJaxMap['math_84'] = 'w/s';
MathJaxMap['math_85'] = '1/x';
MathJaxMap['math_86'] = 'x';
MathJaxMap['math_87'] = 'a=1, b=−1';
MathJaxMap['math_88'] = 'c=−1';
MathJaxMap['math_89'] = 'ϕ';
MathJaxMap['math_90'] = 'ϕ';
MathJaxMap['math_91'] = 'ϕ';
MathJaxMap['math_92'] = 'ϕ';
MathJaxMap['math_93'] = 'ϕ';
MathJaxMap['math_94'] = '36 mm×24 mm';
MathJaxMap['math_95'] = '3:2=1.5';
MathJaxMap['math_96'] = '16:9≈1.78';
MathJaxMap['math_97'] = '1280×720 pixels';
MathJaxMap['math_98'] = '1920×1080 pixels';
MathJaxMap['math_99'] = '640×480 pixels';
MathJaxMap['math_100'] = '2560×1600 pixels';
MathJaxMap['math_101'] = 'ϕ=1.618033…';
MathJaxMap['math_102'] = 'ϕ';
MathJaxMap['math_103'] = 'n';
MathJaxMap['math_104'] = 'Fn/Fn−1';
MathJaxMap['math_105'] = 'x';
MathJaxMap['math_106'] = 'Fn−2/Fn−1';
MathJaxMap['math_107'] = '1/x';
MathJaxMap['math_108'] = 'x';
MathJaxMap['math_109'] = '1/x';
MathJaxMap['math_110'] = 'x';
MathJaxMap['math_111'] = 'x2−x−1=0';
MathJaxMap['math_112'] = 'ϕ';
MathJaxMap['math_113'] = '1−ϕ';
MathJaxMap['math_114'] = 'ϕ';
MathJaxMap['math_115'] = 'ϕ';
MathJaxMap['math_116'] = '=glide';
MathJaxMap['math_117'] = 'c7';
MathJaxMap['math_118'] = 'cn';
MathJaxMap['math_119'] = 'dn';
MathJaxMap['math_120'] = 'n';
MathJaxMap['math_121'] = 'dn';
MathJaxMap['math_122'] = 'n';
MathJaxMap['math_123'] = 'd21';
MathJaxMap['math_124'] = 'c7';
MathJaxMap['math_125'] = 'p';
MathJaxMap['math_126'] = 'b';
MathJaxMap['math_127'] = 'p';
MathJaxMap['math_128'] = 'b';
MathJaxMap['math_129'] = 'c';
MathJaxMap['math_130'] = 'p';
MathJaxMap['math_131'] = 'm';
MathJaxMap['math_132'] = 'g';
MathJaxMap['math_133'] = 'm';
MathJaxMap['math_134'] = 'g';
MathJaxMap['math_135'] = 'pma2';
MathJaxMap['math_136'] = 'p';
MathJaxMap['math_137'] = 'm';
MathJaxMap['math_138'] = 'm';
MathJaxMap['math_139'] = 'a';
MathJaxMap['math_140'] = 'p1__ __';
MathJaxMap['math_141'] = 'p11_';
MathJaxMap['math_142'] = 'p111';
MathJaxMap['math_143'] = 'p1_ _';
MathJaxMap['math_144'] = 'p1m1';
MathJaxMap['math_145'] = 'pm_ _';
MathJaxMap['math_146'] = 'pma2';
MathJaxMap['math_147'] = 'p111';
MathJaxMap['math_148'] = 'p112';
MathJaxMap['math_149'] = 'p112';
MathJaxMap['math_150'] = 'p112';
MathJaxMap['math_151'] = 'pmm2';
MathJaxMap['math_152'] = 'A';
MathJaxMap['math_153'] = 'B';
MathJaxMap['math_154'] = 'C';
MathJaxMap['math_155'] = 'A';
MathJaxMap['math_156'] = 'B';
MathJaxMap['math_157'] = 'C';
MathJaxMap['math_158'] = 'B';
MathJaxMap['math_159'] = 'C';
MathJaxMap['math_160'] = 'A';
MathJaxMap['math_161'] = 'B';
MathJaxMap['math_162'] = 'C';
MathJaxMap['math_163'] = 'I';
MathJaxMap['math_164'] = 'R';
MathJaxMap['math_165'] = 'V';
MathJaxMap['math_166'] = 'H';
MathJaxMap['math_167'] = 'V';
MathJaxMap['math_168'] = 'H';
MathJaxMap['math_169'] = 'VH';
MathJaxMap['math_170'] = 'R';
MathJaxMap['math_171'] = 'VH=R';
MathJaxMap['math_172'] = 'A';
MathJaxMap['math_173'] = 'I';
MathJaxMap['math_174'] = '180°';
MathJaxMap['math_175'] = 'RR=I';
MathJaxMap['math_176'] = 'RHV=(RH)V=R(HV)';
MathJaxMap['math_177'] = 'R';
MathJaxMap['math_178'] = 'H';
MathJaxMap['math_179'] = 'V';
MathJaxMap['math_180'] = 'x';
MathJaxMap['math_181'] = '1/x';
MathJaxMap['math_182'] = '2×3×4';
MathJaxMap['math_183'] = '2×(3×4)=2×12';
MathJaxMap['math_184'] = '(2×3)×4=6×4';
MathJaxMap['math_185'] = 'A, B,…';
MathJaxMap['math_186'] = 'A∘B';
MathJaxMap['math_187'] = 'I';
MathJaxMap['math_188'] = 'I∘A=A';
MathJaxMap['math_189'] = 'A∘I=A';
MathJaxMap['math_190'] = 'A';
MathJaxMap['math_191'] = 'A−1';
MathJaxMap['math_192'] = 'A∘A−1=I';
MathJaxMap['math_193'] = 'A−1∘A=I';
MathJaxMap['math_194'] = 'A∘B∘C=A∘(B∘C)=(A∘B)∘C';
MathJaxMap['math_195'] = 'A▲B=B';
MathJaxMap['math_196'] = 'C▲B=A';
MathJaxMap['math_197'] = 'X ▲ Y ▲ Z';
MathJaxMap['math_198'] = '(A ▲ B) ▲ C=B ▲ C=A';
MathJaxMap['math_199'] = 'A ▲ (B ▲ C)=A ▲ A=A';
MathJaxMap['math_200'] = '33=27';
MathJaxMap['math_201'] = 'B ▲ C';
MathJaxMap['math_202'] = 'B ▲ C=A';
MathJaxMap['math_203'] = 'F';
MathJaxMap['math_204'] = 'R';
MathJaxMap['math_205'] = 'T';
MathJaxMap['math_206'] = 'F';
MathJaxMap['math_207'] = 'R';
MathJaxMap['math_208'] = 'P';
MathJaxMap['math_209'] = 'I';
MathJaxMap['math_210'] = 'I';
MathJaxMap['math_211'] = 'F';
MathJaxMap['math_212'] = 'R';
MathJaxMap['math_213'] = 'P';
MathJaxMap['math_214'] = 'R';
MathJaxMap['math_215'] = 'T';
MathJaxMap['math_216'] = 'F';
MathJaxMap['math_217'] = 'I';
MathJaxMap['math_218'] = 'I';
MathJaxMap['math_219'] = 'T';
MathJaxMap['math_220'] = 'T∘T';
MathJaxMap['math_221'] = 'T2';
MathJaxMap['math_222'] = 'T∘T∘T=T3';
MathJaxMap['math_223'] = 'T2';
MathJaxMap['math_224'] = 'T';
MathJaxMap['math_225'] = 'T−1';
MathJaxMap['math_226'] = 'T−1∘T−1';
MathJaxMap['math_227'] = 'T−2';
MathJaxMap['math_228'] = 'T−1∘T−1∘T−1=T−3';
MathJaxMap['math_229'] = 'I';
MathJaxMap['math_230'] = 'T0';
MathJaxMap['math_231'] = 'T';
MathJaxMap['math_232'] = '〈T〉';
MathJaxMap['math_233'] = 'G';
MathJaxMap['math_234'] = 'G2=T';
MathJaxMap['math_235'] = 'G∘T=T∘G';
MathJaxMap['math_236'] = 'V';
MathJaxMap['math_237'] = 'V';
MathJaxMap['math_238'] = 'T';
MathJaxMap['math_239'] = 'V';
MathJaxMap['math_240'] = 'T';
MathJaxMap['math_241'] = 'V';
MathJaxMap['math_242'] = 'T';
MathJaxMap['math_243'] = 'TV=T∘V';
MathJaxMap['math_244'] = 'V';
MathJaxMap['math_245'] = 'T';
MathJaxMap['math_246'] = 'We';
MathJaxMap['math_247'] = 'A∘B=B∘A';
MathJaxMap['math_248'] = 'ab=b+a; a×b=b×a';
MathJaxMap['math_249'] = 'VT=TV';
MathJaxMap['math_250'] = 'VT=T−1V';
MathJaxMap['math_251'] = 'VT=T−1V';
MathJaxMap['math_252'] = 'd1';
MathJaxMap['math_253'] = 'c2';
MathJaxMap['math_254'] = 'c1,c2,d1,';
MathJaxMap['math_255'] = 'd2';
MathJaxMap['math_256'] = 'd5';
MathJaxMap['math_257'] = 'd5';
MathJaxMap['math_258'] = 'a';
MathJaxMap['math_259'] = 'b';
MathJaxMap['math_260'] = 'ab';
MathJaxMap['math_261'] = 'ϕ=1+52≈1.618033';
MathJaxMap['math_262'] = 'S';
MathJaxMap['math_263'] = 'AAA';
MathJaxMap['math_264'] = 'pm11';
MathJaxMap['math_265'] = 'pma2';
MathJaxMap['math_266'] = '{I,V,H,R2,R3,D1,D2}';
MathJaxMap['math_267'] = 'H';
MathJaxMap['math_268'] = 'V';
MathJaxMap['math_269'] = 'R';
MathJaxMap['math_270'] = 'D1';
MathJaxMap['math_271'] = 'D1';
MathJaxMap['math_272'] = 'VT';
MathJaxMap['math_273'] = 'T−1V';
MathJaxMap['math_274'] = 'WeWdWcWbWa…';
MathJaxMap['math_275'] = 'Wb';
MathJaxMap['math_276'] = 'V';
MathJaxMap['math_277'] = 'ZZZZZZZZZ';
MathJaxMap['math_278'] = 'UUUUUUUUU';
MathJaxMap['math_279'] = 'p';
MathJaxMap['math_280'] = 'm';
MathJaxMap['math_281'] = 'pmm2';
MathJaxMap['math_282'] = 'ϕ=(1+5)/2';
MathJaxMap['math_283'] = 'x2';
MathJaxMap['math_284'] = ' 1/x';
MathJaxMap['math_285'] = 'φ2=φ+1';
MathJaxMap['math_286'] = '1/φ=φ−1';
MathJaxMap['math_287'] = 'φ';
MathJaxMap['math_288'] = 'x2=x+1';
MathJaxMap['math_289'] = '(1−ϕ)';
MathJaxMap['math_290'] = '(1−ϕ)';
MathJaxMap['math_291'] = 'ℓ=6/(2+2φ)≈1.15';
MathJaxMap['math_292'] = 'φℓ≈1.85';
MathJaxMap['math_293'] = 'F0';
MathJaxMap['math_294'] = 'F0+F1=F2';
MathJaxMap['math_295'] = 'F0+1=1';
MathJaxMap['math_296'] = 'F0=0';
MathJaxMap['math_297'] = 'F−1,F−2,…,F−6';
MathJaxMap['math_298'] = 'n';
MathJaxMap['math_299'] = 'Ln';
MathJaxMap['math_300'] = 'L3';
MathJaxMap['math_301'] = 'L10';
MathJaxMap['math_302'] = 'φ';
MathJaxMap['math_303'] = 'φ';
MathJaxMap['math_304'] = 'n';
MathJaxMap['math_305'] = 'n';
MathJaxMap['math_306'] = 'n=1';
MathJaxMap['math_307'] = 'n=2';
MathJaxMap['math_308'] = 'F5';
MathJaxMap['math_309'] = 'n';
MathJaxMap['math_310'] = 'F13';
MathJaxMap['math_311'] = 'x';
MathJaxMap['math_312'] = 'y';
MathJaxMap['math_313'] = 'x';
MathJaxMap['math_314'] = 'y';
MathJaxMap['math_315'] = '(x+y)/2<xy';
MathJaxMap['math_316'] = 'x=y';
MathJaxMap['math_317'] = 'x';
MathJaxMap['math_318'] = 'y';
MathJaxMap['math_319'] = 'H≤G≤A';
MathJaxMap['math_320'] = 'H';
MathJaxMap['math_321'] = 'G';
MathJaxMap['math_322'] = 'A';
MathJaxMap['math_323'] = 'A=1x';
MathJaxMap['math_324'] = 'B=1y';
MathJaxMap['math_325'] = 'x';
MathJaxMap['math_326'] = 'y';
MathJaxMap['math_327'] = 'A';
MathJaxMap['math_328'] = 'B';
MathJaxMap['math_329'] = 'x';
MathJaxMap['math_330'] = 'y';
MathJaxMap['math_331'] = 'A';
MathJaxMap['math_332'] = 'B';
MathJaxMap['math_333'] = 'A';
MathJaxMap['math_334'] = 'B';
MathJaxMap['math_335'] = 'n';
MathJaxMap['math_336'] = 'n';
MathJaxMap['math_337'] = 'n=1,2,3,4,5';
MathJaxMap['math_338'] = '1, 2, 3, 5, 8, ..., Fn+1';
MathJaxMap['math_339'] = 'm';
MathJaxMap['math_340'] = 'n';
MathJaxMap['math_341'] = '5m+8n';
MathJaxMap['math_342'] = '55m+88n';
MathJaxMap['math_343'] = 'n';
MathJaxMap['math_344'] = 'n';
MathJaxMap['math_345'] = 'Bn';
MathJaxMap['math_346'] = 'x';
MathJaxMap['math_347'] = 'x';
MathJaxMap['math_348'] = 'n';
MathJaxMap['math_349'] = 'Bn+1≈xBn≈x2Bn−1';
MathJaxMap['math_350'] = 'Bn−1';
MathJaxMap['math_351'] = 'x2=x+2';
MathJaxMap['math_352'] = 'x';
MathJaxMap['math_353'] = '3Bn';
MathJaxMap['math_354'] = '2n';
MathJaxMap['math_355'] = 'Bn';
MathJaxMap['math_356'] = 'Bn=Bn−1+2Bn−2';
MathJaxMap['math_357'] = 'x=2, −1';
MathJaxMap['math_358'] = '−1';
MathJaxMap['math_359'] = 'Bn=[2n−(−1)n]/3';
MathJaxMap['math_360'] = 'q';
MathJaxMap['math_361'] = 'x2−x−1';
MathJaxMap['math_362'] = 'x2−mx−1';
MathJaxMap['math_363'] = 'm=1,2,3…';
MathJaxMap['math_364'] = 'm=1,2,3,4';
MathJaxMap['math_365'] = 'm';
MathJaxMap['math_366'] = '1+2≈2.414';
MathJaxMap['math_367'] = '12(3+13)≈3.303';
MathJaxMap['math_368'] = '2+5≈4.236';
MathJaxMap['math_369'] = '12(5+29)≈5.193';
MathJaxMap['math_370'] = '12(m+m2+4)';
MathJaxMap['math_371'] = 'G';
MathJaxMap['math_372'] = 'p';
MathJaxMap['math_373'] = 'q';
MathJaxMap['math_374'] = 'p=q=1';
MathJaxMap['math_375'] = 'p';
MathJaxMap['math_376'] = 'q';
MathJaxMap['math_377'] = 'Gn+1';
MathJaxMap['math_378'] = 'Gn';
MathJaxMap['math_379'] = 'Gn+1/Gn';
MathJaxMap['math_380'] = 'Gn/Gn−1';
MathJaxMap['math_381'] = 'x';
MathJaxMap['math_382'] = 'n';
MathJaxMap['math_383'] = 'x';
MathJaxMap['math_384'] = 'x';
MathJaxMap['math_385'] = 'p';
MathJaxMap['math_386'] = 'q';
MathJaxMap['math_387'] = 'A';
MathJaxMap['math_388'] = 'B';
MathJaxMap['math_389'] = 'C';
MathJaxMap['math_390'] = 'A';
MathJaxMap['math_391'] = 'B';
MathJaxMap['math_392'] = 'C';
MathJaxMap['math_393'] = 'B';
MathJaxMap['math_394'] = 'A';
MathJaxMap['math_395'] = 'C';
MathJaxMap['math_396'] = 'B';
MathJaxMap['math_397'] = 'A';
MathJaxMap['math_398'] = 'C';
MathJaxMap['math_399'] = 'A';
MathJaxMap['math_400'] = 'B';
MathJaxMap['math_401'] = 'C';
MathJaxMap['math_402'] = 'D';
MathJaxMap['math_403'] = 'A′,B′,C′';
MathJaxMap['math_404'] = 'D′';
MathJaxMap['math_405'] = 'd5';
MathJaxMap['math_406'] = 'c5';
MathJaxMap['math_407'] = 'd5';
MathJaxMap['math_408'] = 'd4';
MathJaxMap['math_409'] = 'c5';
MathJaxMap['math_410'] = 'd5';
MathJaxMap['math_411'] = 'd20';
MathJaxMap['math_412'] = 'd5';
MathJaxMap['math_413'] = 'c9';
MathJaxMap['math_414'] = 'c6';
MathJaxMap['math_415'] = 'd2';
MathJaxMap['math_416'] = 'd1';
MathJaxMap['math_417'] = 'c4';
MathJaxMap['math_418'] = 'd2';
MathJaxMap['math_419'] = 'p1a1';
MathJaxMap['math_420'] = 'p1m1';
MathJaxMap['math_421'] = 'p111';
MathJaxMap['math_422'] = 'p112';
MathJaxMap['math_423'] = 'pm11';
MathJaxMap['math_424'] = 'pma2';
MathJaxMap['math_425'] = 'pmm2';
MathJaxMap['math_426'] = 'pmm2';
MathJaxMap['math_427'] = 'p1a1';
MathJaxMap['math_428'] = 'pma2';
MathJaxMap['math_429'] = 'p112';
MathJaxMap['math_430'] = 'pmm2';
MathJaxMap['math_431'] = 'p1m1';
MathJaxMap['math_432'] = 'pma2';
MathJaxMap['math_433'] = 'p111';
MathJaxMap['math_434'] = 'pm11';
MathJaxMap['math_435'] = 'pma2';
MathJaxMap['math_436'] = 'p112';
MathJaxMap['math_437'] = 'pmm2';
MathJaxMap['math_438'] = 'pm11';
MathJaxMap['math_439'] = 'p1m1';
MathJaxMap['math_440'] = 'pmm2';
MathJaxMap['math_441'] = 'pmm2';
MathJaxMap['math_442'] = 'pma2';
MathJaxMap['math_443'] = 'p1a1';
MathJaxMap['math_444'] = 'p4m';
MathJaxMap['math_445'] = 'p4';
MathJaxMap['math_446'] = 'p4m';
MathJaxMap['math_447'] = 'p4m';
MathJaxMap['math_448'] = 'cmm';
MathJaxMap['math_449'] = 'p4g';
MathJaxMap['math_450'] = 'p4';
MathJaxMap['math_451'] = 'cm';
MathJaxMap['math_452'] = 'cmm';
MathJaxMap['math_453'] = 'pg';
MathJaxMap['math_454'] = 'p1';
MathJaxMap['math_455'] = 'p6';
MathJaxMap['math_456'] = 'p3';
MathJaxMap['math_457'] = 'a';
MathJaxMap['math_458'] = 'n';
MathJaxMap['math_459'] = 'a';
MathJaxMap['math_460'] = 'n';
MathJaxMap['math_461'] = 'a';
MathJaxMap['math_462'] = 'n';
MathJaxMap['math_463'] = '23 mod 4 = 3';
MathJaxMap['math_464'] = '23=5×4+3';
MathJaxMap['math_465'] = 'a⊕b=(a+b)';
MathJaxMap['math_466'] = 'A';
MathJaxMap['math_467'] = 'B';
MathJaxMap['math_468'] = 'C';
MathJaxMap['math_469'] = 'A';
MathJaxMap['math_470'] = 'B';
MathJaxMap['math_471'] = 'B';
MathJaxMap['math_472'] = 'B';
MathJaxMap['math_473'] = 'B';
MathJaxMap['math_474'] = 'B';
MathJaxMap['math_475'] = 'C';
MathJaxMap['math_476'] = 'A';
MathJaxMap['math_477'] = 'C';
MathJaxMap['math_478'] = 'C';
MathJaxMap['math_479'] = 'A';
MathJaxMap['math_480'] = 'B';
MathJaxMap['math_481'] = 'A';
MathJaxMap['math_482'] = 'B';
MathJaxMap['math_483'] = 'C';
MathJaxMap['math_484'] = 'D';
MathJaxMap['math_485'] = 'E';
MathJaxMap['math_486'] = 'F';
MathJaxMap['math_487'] = 'A';
MathJaxMap['math_488'] = 'A';
MathJaxMap['math_489'] = 'B';
MathJaxMap['math_490'] = 'C';
MathJaxMap['math_491'] = 'D';
MathJaxMap['math_492'] = 'E';
MathJaxMap['math_493'] = 'F';
MathJaxMap['math_494'] = 'B';
MathJaxMap['math_495'] = 'B';
MathJaxMap['math_496'] = 'A';
MathJaxMap['math_497'] = 'D';
MathJaxMap['math_498'] = 'C';
MathJaxMap['math_499'] = 'F';
MathJaxMap['math_500'] = 'E';
MathJaxMap['math_501'] = 'C';
MathJaxMap['math_502'] = 'C';
MathJaxMap['math_503'] = 'E';
MathJaxMap['math_504'] = 'A';
MathJaxMap['math_505'] = 'F';
MathJaxMap['math_506'] = 'B';
MathJaxMap['math_507'] = 'D';
MathJaxMap['math_508'] = 'D';
MathJaxMap['math_509'] = 'D';
MathJaxMap['math_510'] = 'F';
MathJaxMap['math_511'] = 'B';
MathJaxMap['math_512'] = 'E';
MathJaxMap['math_513'] = 'A';
MathJaxMap['math_514'] = 'C';
MathJaxMap['math_515'] = 'E';
MathJaxMap['math_516'] = 'E';
MathJaxMap['math_517'] = 'C';
MathJaxMap['math_518'] = 'F';
MathJaxMap['math_519'] = 'A';
MathJaxMap['math_520'] = 'D';
MathJaxMap['math_521'] = 'B';
MathJaxMap['math_522'] = 'F';
MathJaxMap['math_523'] = 'F';
MathJaxMap['math_524'] = 'D';
MathJaxMap['math_525'] = 'E';
MathJaxMap['math_526'] = 'B';
MathJaxMap['math_527'] = 'C';
MathJaxMap['math_528'] = 'A';
MathJaxMap['math_529'] = 'F';
MathJaxMap['math_530'] = 'E';
MathJaxMap['math_531'] = 'E';
MathJaxMap['math_532'] = 'F';
MathJaxMap['math_533'] = 'F';
MathJaxMap['math_534'] = 'R';
MathJaxMap['math_535'] = 'F';
MathJaxMap['math_536'] = 'R';
MathJaxMap['math_537'] = 'F';
MathJaxMap['math_538'] = 'R';
MathJaxMap['math_539'] = '76 in. × 80 in.';
MathJaxMap['math_540'] = 'd4';
MathJaxMap['math_541'] = 'CW = 2341, CCW = 4123, CWcross = 2413, and CCWcross = 3142';
MathJaxMap['math_542'] = 'd2';
MathJaxMap['math_543'] = 'R';
MathJaxMap['math_544'] = 'V';
MathJaxMap['math_545'] = 'H';
MathJaxMap['math_546'] = '{I,R,V,H}';
MathJaxMap['math_547'] = '{I,R,R2,R3,H,V,RH=VR,RV=HR}';
MathJaxMap['math_548'] = 'R';
MathJaxMap['math_549'] = '<T, R|R2=I,T ο R=R ο T−1>={..., T−1, I, T1, ...; ...R ο T−1, R, R ο T1,...}';
MathJaxMap['math_550'] = '<T, R, H|R2 = H2=I,T ο H=H ο T, R ο H=H ο R,(R ο T)2=I>={..., T−1, I, T1, ...; ...,R ο T−1, R, R ο T,...; ...,H ο T−1, H, H ο T, ...;...,R ο H ο T−1,R ο H,R ο H ο T,...}';
MathJaxMap['math_551'] = 'd8';
MathJaxMap['math_552'] = 'c8';
MathJaxMap['math_553'] = '<R|R8=I>={I, R, R2, R3, R4, R5, R6, R7}';
MathJaxMap['math_554'] = 'R';
MathJaxMap['math_555'] = '8×13';
MathJaxMap['math_556'] = 'p1m1';
MathJaxMap['math_557'] = 'p4';
MathJaxMap['math_558'] = 'd3';
MathJaxMap['math_559'] = 'p3';
MathJaxMap['math_560'] = 'R';
MathJaxMap['math_561'] = 'V';
MathJaxMap['math_562'] = '{I, R, R2, V, VR=R2V, VR2=RV}';
MathJaxMap['math_563'] = 'A, B';
MathJaxMap['math_564'] = 'C';