Revision #563 → #1269 · back to history
addedGolden ratio (lead definition)15899c69e484
addedGolden rectangle cut into square and similar rectangle21b92a80609b
addedGolden ratio of two quantities4d3159f61e0e
addedPositive root is the golden ratio2a0eae308148
addedEuclid's extreme and mean ratio60f9764c1d29
addedIrrationality of the golden ratiod4c5b6f01c84
addedIrrationality via lowest-terms contradictionb4dec17d1f6d
addedIrrationality via sqrt(5)b6dea12d6ddc
addedMinimal polynomial of the golden ratiodf1ac2fba62e
addedBoth roots are algebraic integers3e8e1be6b894
addedGolden ratio as fundamental unit of golden field783158ef52c5
addedGolden ratio is constructible6e0337921756
addedUnique property among positive numbers72baee029703
addedPowers satisfy Fibonacci-like recurrence6eb9627be70b
addedSimple continued fraction expansion6672564b3157
addedHurwitz inequality for Diophantine approximationse066d2c4f7f3
addedContinued square root forma02089c66c52
addedFibonacci sequence recurrence5bac6c5d106a
addedLucas numbersb5a61feace1c
addedGolden ratio as limit of Fibonacci/Lucas ratiosd51bb962849f
addedClosed-form (Binet's) expressions296d49885fb8
addedLimit of Lucas/Fibonacci quotient equals sqrt(5)9b5a71a66ede
addedPowers obey Fibonacci recurrence2a86ead21e68
addedSum of third consecutive Fibonacci is Lucas328a62724e9f
addedConstruction by interior division16dd860d1699
addedConstruction by exterior division2ba44c2cd0c9
addedGolden angle27a4ea1c60bd
addedDiagonal-to-side ratio of regular pentagon7adccd307d95
addedGolden triangle (sublime triangle)4b188b9438df
addedGolden gnomon2088155245d4
addedBisection subdivides golden triangle5fe38cfd8cbb
addedTrisection subdivides golden gnomon424ddf6a6dd3
addedOdom's construction from equilateral triangle5d6f1f376e48
addedKepler triangle26eca3acb2a9
addedMaximum inradius-to-side ratio isosceles trianglea01da0482558
addedGolden rectanglecae086142f4c
addedGolden rhombus248e371a77c1
addedVesica piscis golden subdivisione560d019daa3
addedGolden spiralcf0466f615a2
addedThree golden rectangles form Borromean ringsb68b65c642d7
addedCube inscribed in dodecahedronf94ded818380
addedNewton's method computation time0351494c5bff
addedFifth roots of unity sum is quadratic integer7cb2d0f19a5b
addedGamma function equation solutions6be89ad0250e
addedTerminating representations in golden basea7584084aa0c
addedGolden ratio in hyperbolic geometry648beeaf6539
addedGolden ratio in modular functions38110a6d8752
addedGolden ratio is a Pisot–Vijayaraghavan number1aa7a1f5cad3