Mathematical & Geometric extensions to Pythagoras' Theorem
Bonzai tree: linear branching model
Spiral
Using the proportional values of 1 : 2 : 2.236067977
TABLES OF PYTHAGORAS
1 : 2 : 2.236067977
Based on the pyramid complex at Giza
TABLE-3 LINEAR SERIES: from 1 to infinity
| n | S1 | S2 | S3 |
| 1 | 1 | 2 | 2.236067977 |
| 2 | 2.236067977 | 4.472135955 | 5 |
| 3 | 5 | 10 | 11.180339887 |
| 4 | 11.180339887 | 22.360679775 | 25 |
| 5 | 25 | 50 | 55.901699437 |
| 6 | 55.901699437 | 111.803398875 | 125 |
| 7 | 125 | 250 | 279.508497187 |
| 8 | 279.508497187 | 559.016994375 | 625 |
| 9 | 625 | 1250 | 1397.542485937 |
| 10 | 1397.542485937 | 2795.084971875 | 3125 |
| 11 | 3125 | 6250 | 6987.712429687 |
| 12 | 6987.712429687 | 13975.424859374 | 15625 |
| 13 | 15625 | 31250 | 34938.562148434 |
| 14 | 34938.562148434 | 69877.124296868 | 78125 |
| 15 | 78125 | 156250 | 174692.810742171 |
| 16 | 174692.810742171 | 349385.621484342 | 390625 |
| 17 | 390625 | 781250.000000001 | 873464.053710856 |
| 18 | 873464.053710856 | 1746928.107421712 | 1953125.000000002 |
| 19 | 1953125.000000002 | 3906250.000000003 | 4367320.268554281 |
| 20 | 4367320.268554281 | 8734640.537108561 | 9765625.000000009 |
| 21 | 9765625.000000009 | 19531250.000000019 | 21836601.342771407 |
TABLE-4 LINEAR SERIES: from 1 to zero
| n | S1 | S2 | S3 |
| 1 | 1 | 2 | 2.236067977 |
| 0 | 0.894427191 | 1.788854382 | 2 |
| -1 | 0.8 | 1.6 | 1.788854382 |
| -2 | 0.715541753 | 1.431083506 | 1.6 |
| -3 | 0.64 | 1.28 | 1.431083506 |
| -4 | 0.572433402 | 1.144866804 | 1.28 |
| -5 | 0.512 | 1.024 | 1.144866804 |
| -6 | 0.457946722 | 0.915893444 | 1.024 |
| -7 | 0.4096 | 0.8192 | 0.915893444 |
| -8 | 0.366357377 | 0.732714755 | 0.8192 |
| -9 | 0.32768 | 0.65536 | 0.732714755 |
| -10 | 0.293085902 | 0.586171804 | 0.65536 |
| -11 | 0.262144 | 0.524288 | 0.586171804 |
| -12 | 0.234468722 | 0.468937443 | 0.524288 |
| -13 | 0.2097152 | 0.4194304 | 0.468937443 |
| -14 | 0.187574977 | 0.375149954 | 0.4194304 |
| -15 | 0.16777216 | 0.33554432 | 0.375149954 |
| -16 | 0.150059982 | 0.300119964 | 0.33554432 |
| -17 | 0.134217728 | 0.268435456 | 0.300119964 |
| -18 | 0.120047985 | 0.240095971 | 0.268435456 |
| -19 | 0.107374182 | 0.214748365 | 0.240095971 |
| -20 | 0.096038388 | 0.192076777 | 0.214748365 |
| -21 | 0.085899346 | 0.171798692 | 0.192076777 |
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