Ipersfera: differenze tra le versioni

! Numero di dimensioni ''n'' !! Misura ipersuperficialedell'<math>n</math>-sfera <math> S_n(r) </math> !! Ipervolume <math>(n+1)</math>-dimensionale racchiuso <math> V_{n+1}(r) </math> !! Valore numerico <math> S_n(1) </math> !! Valore numerico <math> V_{n+1}(1) </math>

! 1 !! <math> 2 \pi r </math> !! <math> \pi r^2 </math> !! 6,283.185.307 !! 3,141.592.654

! 2 !! <math> 4 \pi r^2 </math> !! <math> \frac{4}{3} \pi r^3</math> !! 12,566.370.614 !! 4,188.790.205

! 3 !! <math> 2 \pi^2 r^3 </math> !! <math> \frac{1}{2} \pi^2 r^4 </math> !!19,739.208.802 !! 4,934.802.201

! 4 !! <math> \frac{8}{3} \pi^2 r^4 </math> !! <math> \frac{8}{15} \pi^2 r^5 </math> !! 26,318.945.070 !! 5,263.789.014

! 5 !! <math> \pi^3 r^5 </math> !! <math> \frac{1}{6} \pi^3 r^6 </math> !! 31,006.276.680 !! 5,167.712.780

! 6 !! <math> \frac{16}{15} \pi^3 r^6 </math> !! <math> \frac{16}{105} \pi^3 r^7 </math> !! 33,073.361.792 !! 4,724.765.970

! 7 !! <math> \frac{1}{3} \pi^4 r^7 </math> !! <math> \frac{1}{24} \pi^4 r^8 </math> !! 32,469.697.011 !! 4,058.712.126

! 8 !! <math> \frac{32}{105} \pi^4 r^8 </math> !! <math> \frac{32}{945} \pi^4 r^9 </math> !! 29,686.580.125 !! 3,298.508.903

! 9 !! <math> \frac{1}{12} \pi^5 r^9 </math> !! <math> \frac{1}{120} \pi^5 r^{10} </math !! 25,501.640.399 !! 2,550.164.040

! 10 !! <math> \frac{64}{945} \pi^5 r^{10} </math> !! <math> \frac{64}{10.395} \pi^5 r^{11} </math> !! 20,725.142.673 !! 1,884.103.879

! 11 !! <math> \frac{1}{60} \pi^6 r^{11} </math> !! <math> \frac{1}{720} \pi^6 r^{12} </math> !! 16,023.153.226 !! 1,335.262.769

! 12 !! <math> \frac{128}{10.395} \pi^6 r^{12} </math> !! <math> \frac{128}{135.135} \pi^6 r^{13} </math> !! 11,838.173.812 !! 0,910.628.755

! 13 !! <math> \frac{1}{360} \pi^7 r^{13} </math> !! <math> \frac{1}{5.040} \pi^7 r^{14} </math> !! 8,389.703.410 !! 0,599.264.529

! 14 !! <math> \frac{256}{135.135} \pi^7 r^{14} </math> !! <math> \frac{256}{2.027.025} \pi^7 r^{15} </math> !! 5,721.649.212 !! 0,381.443.281

! 15 !! <math> \frac{1}{2.520} \pi^8 r^{15} </math> !! <math> \frac{1}{40.320} \pi^8 r^{16} </math> !! 3,765.290.086 !! 0,235.330.630

! 16 !! <math> \frac{512}{2.027.025} \pi^8 r^{16} </math> !! <math> \frac{512}{34.459.425} \pi^8 r^{17} </math> !! 2,396.678.818 !! 0,140.981.107

! 17 !! <math> \frac{1}{20.160} \pi^9 r^{17} </math> !! <math> \frac{1}{362.880} \pi^9 r^{18} </math> !! 1,478.625.959 !! 0,082.145.887

! 18 !! <math> \frac{1.024}{34.459.425} \pi^9 r^{18} </math> !! <math> \frac{1.024}{654.729.075} \pi^9 r^{19} </math> !! 0,885.810.420 !! 0,046.621.601

! 19 !! <math> \frac{1}{181.440} \pi^{10} r^{19} </math> !! <math> \frac{1}{3.628.800} \pi^{10} r^{20} </math> !! 0,516.137.828 !! 0,025.806.891

! 20 !! <math> \frac{2.048}{654.729.075} \pi^{10} r^{20} </math> !! <math> \frac{2.048}{13.749.310.575} \pi^{10} r^{21} </math> !! 0,292.932.159 !! 0,0139.491.504