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Fungrim entry: d774fe

(a+ba=ab)        (ab=φ)\left(\frac{a + b}{a} = \frac{a}{b}\right) \;\implies\; \left(\frac{a}{b} = \varphi\right)
Assumptions:a(0,)  and  b(0,)a \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left(0, \infty\right)
\left(\frac{a + b}{a} = \frac{a}{b}\right) \;\implies\; \left(\frac{a}{b} = \varphi\right)

a \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left(0, \infty\right)
Fungrim symbol Notation Short description
GoldenRatioφ\varphi The golden ratio (1.618...)
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Implies(Equal(Div(Add(a, b), a), Div(a, b)), Equal(Div(a, b), GoldenRatio))),
    Variables(a, b),
    Assumptions(And(Element(a, OpenInterval(0, Infinity)), Element(b, OpenInterval(0, Infinity)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC