History of Golden ratio

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when	who	what
2026-08-17 11:22	bmatschke	the conjugate column names the number rather than stating an equation, and the formula drops a sentence that repeats it	current reviewed
2026-08-16 16:56	bmatschke	phi_inv held the conjugate root: its sign was wrong, and so were the two formulas that said phi^-1 is a root of x^2-x-1. The value is kept as phi_conj, which is what it is.
2026-08-15 11:02	bmatschke	how well the digits are known: proven (verified here against (1+sqrt(5))/2 in ball arithmetic)
2026-08-09 09:25	label hoist	moved the parameter labels onto the parameter they describe
2026-08-09 09:11	flattening	entries rewritten as records with named parameters
2026-08-09 08:34	data-repository import	the current state of the data repository
2021-03-18 17:20	bmatschke	from the data repository, d2a214fd
2021-03-17 20:28	bmatschke	from the data repository, 491ea040
2021-03-17 20:22	bmatschke	from the data repository, ac909da9

What changed between 2026-08-15 11:02 and 2026-08-16 16:56

from line 9 (5 lines, 1 more than before) @@ -9,4 +9,5 @@

       phi: $\varphi$       phi_inv: $\varphi^{-1}$+      phi_conj: $\hat{\varphi} = 1-\varphi$ Comments:   comment-golden-ratio: $\varphi$ equals the ratio $a/b$  of those positive real numbers

from line 15 (8 lines, 2 more than before) @@ -14,6 +15,8 @@

 Formulas:   formula-polynomial-root: $\varphi^2-\varphi-1=0$, which has two roots, $\varphi$-    and $\varphi^{-1}$.-  formula-inverse: $\varphi^{-1} = 1 - \varphi$.+    and its conjugate $\hat{\varphi} = 1-\varphi$.+  formula-inverse: $\varphi^{-1} = \varphi - 1$.+  formula-conjugate: $\hat{\varphi} = -\varphi^{-1} = 1-\varphi$. Note $\varphi^{-1}$+    is positive and $\hat{\varphi}$ is negative; they differ only in sign. Programs:   program-sage:

from line 38 (8 lines, 1 more than before) @@ -35,7 +38,8 @@

   type: R   rigour: proven-  rigour details: Checked here against (1 + sqrt(5))/2 computed in ball arithmetic-    at 400 bits, which agreed to past the hundredth digit. The value is also an algebraic-    number, so any number of further digits can be had on demand.+  rigour details: 'Checked here against ball arithmetic at 4000 bits, which covers+    every stored digit rather than the first hundred: all three entries agree to within+    one unit in the last place of the 300 digits held. The values are algebraic, so+    any number of further digits can be had on demand.' Display properties:   number-header: Golden ratio

from line 50 (6 lines, 3 more than before) @@ -46,3 +50,6 @@

 - params:     expression: phi_inv+  number: '0.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137484754088075386891752126633862223536931793180060766726354433389086595939582905638322661319928290267880675208766892501711696207032221043216269548626296313614438149758701220340805887954454749246185695365'+- params:+    expression: phi_conj   number: '-0.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137484754088075386891752126633862223536931793180060766726354433389086595939582905638322661319928290267880675208766892501711696207032221043216269548626296313614438149758701220340805887954454749246185695365'