Mathematical & Geometric extensions to Pythagoras' Theorem
Using the proportional values of 1 : 2 : 2.236067977
TABLES OF PYTHAGORAS
1 : 2 : 2.236067977
Based on the pyramid complex at Giza
TABLE-2 NESTED SERIES: from 1 to zero
| n | S1 | S2 | S3 |
| 1 | 1 | 2 | 2.236067977 |
| 0 | 0.447213595 | 0.894427191 | 1 |
| -1 | 0.2 | 0.4 | 0.447213595 |
| -2 | 0.089442719 | 0.178885438 | 0.2 |
| -3 | 0.04 | 0.08 | 0.089442719 |
| -4 | 0.017888544 | 0.035777088 | 0.04 |
| -5 | 0.008 | 0.016 | 0.017888544 |
| -6 | 0.003577709 | 0.007155418 | 0.008 |
| -7 | 0.0016 | 0.0032 | 0.003577709 |
| -8 | 0.000715542 | 0.001431084 | 0.0016 |
| -9 | 0.00032 | 0.00064 | 0.000715542 |
| -10 | 0.000143108 | 0.000286217 | 0.00032 |
| -11 | 0.000064 | 0.000128 | 0.000143108 |
| -12 | 0.000028622 | 0.000057243 | 0.000064 |
| -13 | 0.0000128 | 0.0000256 | 0.000028622 |
| -14 | 0.000005724 | 0.000011449 | 0.0000128 |
| -15 | 0.00000256 | 0.00000512 | 0.000005724 |
| -16 | 0.000001145 | 0.00000229 | 0.00000256 |
| -17 | 0.000000512 | 0.000001024 | 0.000001145 |
| -18 | 0.000000229 | 0.000000458 | 0.000000512 |
| -19 | 0.000000102 | 0.000000205 | 0.000000229 |
| -20 | 0.000000046 | 0.000000092 | 0.000000102 |
| -21 | 0.00000002 | 0.000000041 | 0.000000046 |
| -22 | 0.000000009 | 0.000000018 | 0.00000002 |
| -23 | 0.000000004 | 0.000000008 | 0.000000009 |
| -24 | 0.000000002 | 0.000000004 | 0.000000004 |
| -25 | 8.192e-10 | 0.000000002 | 0.000000002 |
| -26 | 3.663573774e-10 | 7.327147549e-10 | 8.192e-10 |
| -27 | 1.6384e-10 | 3.2768e-10 | 3.663573774e-10 |
| -28 | 7.327147549e-11 | 1.46542951e-10 | 1.6384e-10 |
| -29 | 3.2768e-11 | 6.5536e-11 | 7.327147549e-11 |
| -30 | 1.46542951e-11 | 2.930859019e-11 | 3.2768e-11 |
| -31 | 6.5536e-12 | 1.31072e-11 | 1.46542951e-11 |
| -32 | 2.930859019e-12 | 5.861718039e-12 | 6.5536e-12 |
| -33 | 1.31072e-12 | 2.62144e-12 | 2.930859019e-12 |
| -34 | 5.861718039e-13 | 1.172343608e-12 | 1.31072e-12 |
| -35 | 2.62144e-13 | 5.24288e-13 | 5.861718039e-13 |
| -36 | 1.172343608e-13 | 2.344687216e-13 | 2.62144e-13 |
| -37 | 5.24288e-14 | 1.048576e-13 | 1.172343608e-13 |
| -38 | 2.344687216e-14 | 4.689374431e-14 | 5.24288e-14 |
| -39 | 1.048576e-14 | 2.097152e-14 | 2.344687216e-14 |
| -40 | 4.689374431e-15 | 9.378748862e-15 | 1.048576e-14 |
| -41 | 2.097152e-15 | 4.194304e-15 | 4.689374431e-15 |
| -42 | 9.378748862e-16 | 1.875749772e-15 | 2.097152e-15 |
| -43 | 4.194304e-16 | 8.388608e-16 | 9.378748862e-16 |
| -44 | 1.875749772e-16 | 3.751499545e-16 | 4.194304e-16 |
| -45 | 8.388608e-17 | 1.6777216e-16 | 1.875749772e-16 |
| -46 | 3.751499545e-17 | 7.50299909e-17 | 8.388608e-17 |
| -47 | 1.6777216e-17 | 3.3554432e-17 | 3.751499545e-17 |
| -48 | 7.50299909e-18 | 1.500599818e-17 | 1.6777216e-17 |
| -49 | 3.3554432e-18 | 6.7108864e-18 | 7.50299909e-18 |
| -50 | 1.500599818e-18 | 3.001199636e-18 | 3.3554432e-18 |
| -51 | 6.7108864e-19 | 1.34217728e-18 | 1.500599818e-18 |
| -52 | 3.001199636e-19 | 6.002399272e-19 | 6.7108864e-19 |
| -53 | 1.34217728e-19 | 2.68435456e-19 | 3.001199636e-19 |
| -54 | 6.002399272e-20 | 1.200479854e-19 | 1.34217728e-19 |
| -55 | 2.68435456e-20 | 5.36870912e-20 | 6.002399272e-20 |
| -56 | 1.200479854e-20 | 2.400959709e-20 | 2.68435456e-20 |
| -57 | 5.36870912e-21 | 1.073741824e-20 | 1.200479854e-20 |
| -58 | 2.400959709e-21 | 4.801919417e-21 | 5.36870912e-21 |
| -59 | 1.073741824e-21 | 2.147483648e-21 | 2.400959709e-21 |
| -60 | 4.801919417e-22 | 9.603838835e-22 | 1.073741824e-21 |
| -61 | 2.147483648e-22 | 4.294967296e-22 | 4.801919417e-22 |
| -62 | 9.603838835e-23 | 1.920767767e-22 | 2.147483648e-22 |
| -63 | 4.294967296e-23 | 8.589934592e-23 | 9.603838835e-23 |
| -64 | 1.920767767e-23 | 3.841535534e-23 | 4.294967296e-23 |
| -65 | 8.589934592e-24 | 1.717986918e-23 | 1.920767767e-23 |
| -66 | 3.841535534e-24 | 7.683071068e-24 | 8.589934592e-24 |
| -67 | 1.717986918e-24 | 3.435973837e-24 | 3.841535534e-24 |
| -68 | 7.683071068e-25 | 1.536614214e-24 | 1.717986918e-24 |
| -69 | 3.435973837e-25 | 6.871947674e-25 | 7.683071068e-25 |
| -70 | 1.536614214e-25 | 3.073228427e-25 | 3.435973837e-25 |
| -71 | 6.871947674e-26 | 1.374389535e-25 | 1.536614214e-25 |
| -72 | 3.073228427e-26 | 6.146456854e-26 | 6.871947674e-26 |
| -73 | 1.374389535e-26 | 2.748779069e-26 | 3.073228427e-26 |
| -74 | 6.146456854e-27 | 1.229291371e-26 | 1.374389535e-26 |
| -75 | 2.748779069e-27 | 5.497558139e-27 | 6.146456854e-27 |
| -76 | 1.229291371e-27 | 2.458582742e-27 | 2.748779069e-27 |
| -77 | 5.497558139e-28 | 1.099511628e-27 | 1.229291371e-27 |
| -78 | 2.458582742e-28 | 4.917165484e-28 | 5.497558139e-28 |
| -79 | 1.099511628e-28 | 2.199023256e-28 | 2.458582742e-28 |
| -80 | 4.917165484e-29 | 9.834330967e-29 | 1.099511628e-28 |
| -81 | 2.199023256e-29 | 4.398046511e-29 | 4.917165484e-29 |
| -82 | 9.834330967e-30 | 1.966866193e-29 | 2.199023256e-29 |
| -83 | 4.398046511e-30 | 8.796093022e-30 | 9.834330967e-30 |
| -84 | 1.966866193e-30 | 3.933732387e-30 | 4.398046511e-30 |
| -85 | 8.796093022e-31 | 1.759218604e-30 | 1.966866193e-30 |
| -86 | 3.933732387e-31 | 7.867464774e-31 | 8.796093022e-31 |
| -87 | 1.759218604e-31 | 3.518437209e-31 | 3.933732387e-31 |
| -88 | 7.867464774e-32 | 1.573492955e-31 | 1.759218604e-31 |
| -89 | 3.518437209e-32 | 7.036874418e-32 | 7.867464774e-32 |
| -90 | 1.573492955e-32 | 3.146985909e-32 | 3.518437209e-32 |
| -91 | 7.036874418e-33 | 1.407374884e-32 | 1.573492955e-32 |
| -92 | 3.146985909e-33 | 6.293971819e-33 | 7.036874418e-33 |
| -93 | 1.407374884e-33 | 2.814749767e-33 | 3.146985909e-33 |
| -94 | 6.293971819e-34 | 1.258794364e-33 | 1.407374884e-33 |
| -95 | 2.814749767e-34 | 5.629499534e-34 | 6.293971819e-34 |
| -96 | 1.258794364e-34 | 2.517588728e-34 | 2.814749767e-34 |
| -97 | 5.629499534e-35 | 1.125899907e-34 | 1.258794364e-34 |
| -98 | 2.517588728e-35 | 5.035177455e-35 | 5.629499534e-35 |
| -99 | 1.125899907e-35 | 2.251799814e-35 | 2.517588728e-35 |
| -100 | 5.035177455e-36 | 1.007035491e-35 | 1.125899907e-35 |
| -101 | 2.251799814e-36 | 4.503599627e-36 | 5.035177455e-36 |
| -102 | 1.007035491e-36 | 2.014070982e-36 | 2.251799814e-36 |
| -103 | 4.503599627e-37 | 9.007199255e-37 | 1.007035491e-36 |
| -104 | 2.014070982e-37 | 4.028141964e-37 | 4.503599627e-37 |
| -105 | 9.007199255e-38 | 1.801439851e-37 | 2.014070982e-37 |
| -106 | 4.028141964e-38 | 8.056283928e-38 | 9.007199255e-38 |
| -107 | 1.801439851e-38 | 3.602879702e-38 | 4.028141964e-38 |
| -108 | 8.056283928e-39 | 1.611256786e-38 | 1.801439851e-38 |
| -109 | 3.602879702e-39 | 7.205759404e-39 | 8.056283928e-39 |
| -110 | 1.611256786e-39 | 3.222513571e-39 | 3.602879702e-39 |
| -111 | 7.205759404e-40 | 1.441151881e-39 | 1.611256786e-39 |
| -112 | 3.222513571e-40 | 6.445027143e-40 | 7.205759404e-40 |
| -113 | 1.441151881e-40 | 2.882303762e-40 | 3.222513571e-40 |
| -114 | 6.445027143e-41 | 1.289005429e-40 | 1.441151881e-40 |
| -115 | 2.882303762e-41 | 5.764607523e-41 | 6.445027143e-41 |
| -116 | 1.289005429e-41 | 2.578010857e-41 | 2.882303762e-41 |
| -117 | 5.764607523e-42 | 1.152921505e-41 | 1.289005429e-41 |
| -118 | 2.578010857e-42 | 5.156021714e-42 | 5.764607523e-42 |
| -119 | 1.152921505e-42 | 2.305843009e-42 | 2.578010857e-42 |
| -120 | 5.156021714e-43 | 1.031204343e-42 | 1.152921505e-42 |
| -121 | 2.305843009e-43 | 4.611686018e-43 | 5.156021714e-43 |
| -122 | 1.031204343e-43 | 2.062408686e-43 | 2.305843009e-43 |
| -123 | 4.611686018e-44 | 9.223372037e-44 | 1.031204343e-43 |
| -124 | 2.062408686e-44 | 4.124817371e-44 | 4.611686018e-44 |
| -125 | 9.223372037e-45 | 1.844674407e-44 | 2.062408686e-44 |
| -126 | 4.124817371e-45 | 8.249634742e-45 | 9.223372037e-45 |
| -127 | 1.844674407e-45 | 3.689348815e-45 | 4.124817371e-45 |
| -128 | 8.249634742e-46 | 1.649926948e-45 | 1.844674407e-45 |
| -129 | 3.689348815e-46 | 7.378697629e-46 | 8.249634742e-46 |
| -130 | 1.649926948e-46 | 3.299853897e-46 | 3.689348815e-46 |
| -131 | 7.378697629e-47 | 1.475739526e-46 | 1.649926948e-46 |
| -132 | 3.299853897e-47 | 6.599707794e-47 | 7.378697629e-47 |
| -133 | 1.475739526e-47 | 2.951479052e-47 | 3.299853897e-47 |
| -134 | 6.599707794e-48 | 1.319941559e-47 | 1.475739526e-47 |
| -135 | 2.951479052e-48 | 5.902958104e-48 | 6.599707794e-48 |
| -136 | 1.319941559e-48 | 2.639883118e-48 | 2.951479052e-48 |
| -137 | 5.902958104e-49 | 1.180591621e-48 | 1.319941559e-48 |
| -138 | 2.639883118e-49 | 5.279766235e-49 | 5.902958104e-49 |
| -139 | 1.180591621e-49 | 2.361183241e-49 | 2.639883118e-49 |
| -140 | 5.279766235e-50 | 1.055953247e-49 | 1.180591621e-49 |
| -141 | 2.361183241e-50 | 4.722366483e-50 | 5.279766235e-50 |
| -142 | 1.055953247e-50 | 2.111906494e-50 | 2.361183241e-50 |
| -143 | 4.722366483e-51 | 9.444732966e-51 | 1.055953247e-50 |
| -144 | 2.111906494e-51 | 4.223812988e-51 | 4.722366483e-51 |
| -145 | 9.444732966e-52 | 1.888946593e-51 | 2.111906494e-51 |
| -146 | 4.223812988e-52 | 8.447625976e-52 | 9.444732966e-52 |
| -147 | 1.888946593e-52 | 3.777893186e-52 | 4.223812988e-52 |
| -148 | 8.447625976e-53 | 1.689525195e-52 | 1.888946593e-52 |
| -149 | 3.777893186e-53 | 7.555786373e-53 | 8.447625976e-53 |
| -150 | 1.689525195e-53 | 3.379050391e-53 | 3.777893186e-53 |
| -151 | 7.555786373e-54 | 1.511157275e-53 | 1.689525195e-53 |
| -152 | 3.379050391e-54 | 6.758100781e-54 | 7.555786373e-54 |
| -153 | 1.511157275e-54 | 3.022314549e-54 | 3.379050391e-54 |
| -154 | 6.758100781e-55 | 1.351620156e-54 | 1.511157275e-54 |
| -155 | 3.022314549e-55 | 6.044629098e-55 | 6.758100781e-55 |
| -156 | 1.351620156e-55 | 2.703240312e-55 | 3.022314549e-55 |
| -157 | 6.044629098e-56 | 1.20892582e-55 | 1.351620156e-55 |
| -158 | 2.703240312e-56 | 5.406480625e-56 | 6.044629098e-56 |
| -159 | 1.20892582e-56 | 2.417851639e-56 | 2.703240312e-56 |
| -160 | 5.406480625e-57 | 1.081296125e-56 | 1.20892582e-56 |
| -161 | 2.417851639e-57 | 4.835703278e-57 | 5.406480625e-57 |
| -162 | 1.081296125e-57 | 2.16259225e-57 | 2.417851639e-57 |
| -163 | 4.835703278e-58 | 9.671406557e-58 | 1.081296125e-57 |
| -164 | 2.16259225e-58 | 4.3251845e-58 | 4.835703278e-58 |
| -165 | 9.671406557e-59 | 1.934281311e-58 | 2.16259225e-58 |
| -166 | 4.3251845e-59 | 8.650369e-59 | 9.671406557e-59 |
| -167 | 1.934281311e-59 | 3.868562623e-59 | 4.3251845e-59 |
| -168 | 8.650369e-60 | 1.7300738e-59 | 1.934281311e-59 |
| -169 | 3.868562623e-60 | 7.737125246e-60 | 8.650369e-60 |
| -170 | 1.7300738e-60 | 3.4601476e-60 | 3.868562623e-60 |
| -171 | 7.737125246e-61 | 1.547425049e-60 | 1.7300738e-60 |
| -172 | 3.4601476e-61 | 6.9202952e-61 | 7.737125246e-61 |
| -173 | 1.547425049e-61 | 3.094850098e-61 | 3.4601476e-61 |
| -174 | 6.9202952e-62 | 1.38405904e-61 | 1.547425049e-61 |
| -175 | 3.094850098e-62 | 6.189700196e-62 | 6.9202952e-62 |
| -176 | 1.38405904e-62 | 2.76811808e-62 | 3.094850098e-62 |
| -177 | 6.189700196e-63 | 1.237940039e-62 | 1.38405904e-62 |
| -178 | 2.76811808e-63 | 5.53623616e-63 | 6.189700196e-63 |
| -179 | 1.237940039e-63 | 2.475880079e-63 | 2.76811808e-63 |
| -180 | 5.53623616e-64 | 1.107247232e-63 | 1.237940039e-63 |
| -181 | 2.475880079e-64 | 4.951760157e-64 | 5.53623616e-64 |
| -182 | 1.107247232e-64 | 2.214494464e-64 | 2.475880079e-64 |
| -183 | 4.951760157e-65 | 9.903520314e-65 | 1.107247232e-64 |
| -184 | 2.214494464e-65 | 4.428988928e-65 | 4.951760157e-65 |
| -185 | 9.903520314e-66 | 1.980704063e-65 | 2.214494464e-65 |
| -186 | 4.428988928e-66 | 8.857977856e-66 | 9.903520314e-66 |
| -187 | 1.980704063e-66 | 3.961408126e-66 | 4.428988928e-66 |
| -188 | 8.857977856e-67 | 1.771595571e-66 | 1.980704063e-66 |
| -189 | 3.961408126e-67 | 7.922816251e-67 | 8.857977856e-67 |
| -190 | 1.771595571e-67 | 3.543191142e-67 | 3.961408126e-67 |
| -191 | 7.922816251e-68 | 1.58456325e-67 | 1.771595571e-67 |
| -192 | 3.543191142e-68 | 7.086382285e-68 | 7.922816251e-68 |
| -193 | 1.58456325e-68 | 3.169126501e-68 | 3.543191142e-68 |
| -194 | 7.086382285e-69 | 1.417276457e-68 | 1.58456325e-68 |
| -195 | 3.169126501e-69 | 6.338253001e-69 | 7.086382285e-69 |
| -196 | 1.417276457e-69 | 2.834552914e-69 | 3.169126501e-69 |
| -197 | 6.338253001e-70 | 1.2676506e-69 | 1.417276457e-69 |
| -198 | 2.834552914e-70 | 5.669105828e-70 | 6.338253001e-70 |
| -199 | 1.2676506e-70 | 2.5353012e-70 | 2.834552914e-70 |
| -200 | 5.669105828e-71 | 1.133821166e-70 | 1.2676506e-70 |
| -201 | 2.5353012e-71 | 5.070602401e-71 | 5.669105828e-71 |
| -202 | 1.133821166e-71 | 2.267642331e-71 | 2.5353012e-71 |
| -203 | 5.070602401e-72 | 1.01412048e-71 | 1.133821166e-71 |
| -204 | 2.267642331e-72 | 4.535284662e-72 | 5.070602401e-72 |
| -205 | 1.01412048e-72 | 2.02824096e-72 | 2.267642331e-72 |
| -206 | 4.535284662e-73 | 9.070569324e-73 | 1.01412048e-72 |
| -207 | 2.02824096e-73 | 4.056481921e-73 | 4.535284662e-73 |
| -208 | 9.070569324e-74 | 1.814113865e-73 | 2.02824096e-73 |
| -209 | 4.056481921e-74 | 8.112963841e-74 | 9.070569324e-74 |
| -210 | 1.814113865e-74 | 3.62822773e-74 | 4.056481921e-74 |
| -211 | 8.112963841e-75 | 1.622592768e-74 | 1.814113865e-74 |
| -212 | 3.62822773e-75 | 7.256455459e-75 | 8.112963841e-75 |
| -213 | 1.622592768e-75 | 3.245185537e-75 | 3.62822773e-75 |
| -214 | 7.256455459e-76 | 1.451291092e-75 | 1.622592768e-75 |
| -215 | 3.245185537e-76 | 6.490371073e-76 | 7.256455459e-76 |
| -216 | 1.451291092e-76 | 2.902582184e-76 | 3.245185537e-76 |
| -217 | 6.490371073e-77 | 1.298074215e-76 | 1.451291092e-76 |
| -218 | 2.902582184e-77 | 5.805164368e-77 | 6.490371073e-77 |
| -219 | 1.298074215e-77 | 2.596148429e-77 | 2.902582184e-77 |
| -220 | 5.805164368e-78 | 1.161032874e-77 | 1.298074215e-77 |
| -221 | 2.596148429e-78 | 5.192296859e-78 | 5.805164368e-78 |
| -222 | 1.161032874e-78 | 2.322065747e-78 | 2.596148429e-78 |
| -223 | 5.192296859e-79 | 1.038459372e-78 | 1.161032874e-78 |
| -224 | 2.322065747e-79 | 4.644131494e-79 | 5.192296859e-79 |
| -225 | 1.038459372e-79 | 2.076918743e-79 | 2.322065747e-79 |
| -226 | 4.644131494e-80 | 9.288262988e-80 | 1.038459372e-79 |
| -227 | 2.076918743e-80 | 4.153837487e-80 | 4.644131494e-80 |
| -228 | 9.288262988e-81 | 1.857652598e-80 | 2.076918743e-80 |
| -229 | 4.153837487e-81 | 8.307674974e-81 | 9.288262988e-81 |
| -230 | 1.857652598e-81 | 3.715305195e-81 | 4.153837487e-81 |
| -231 | 8.307674974e-82 | 1.661534995e-81 | 1.857652598e-81 |
| -232 | 3.715305195e-82 | 7.43061039e-82 | 8.307674974e-82 |
| -233 | 1.661534995e-82 | 3.323069989e-82 | 3.715305195e-82 |
| -234 | 7.43061039e-83 | 1.486122078e-82 | 1.661534995e-82 |
The Pythagoras Project-Nested series:
Tables of Pythagoras
Nested series: table-1,extended
Nested series: table-2,extended
Linear series: table-3,extended
Linear series: table-4,extended
Other Projects
Copyright 1989
Michael Robinett