# Fungrim entry: d774fe

$\left(\frac{a + b}{a} = \frac{a}{b}\right) \implies \left(\frac{a}{b} = \varphi\right)$
Assumptions:$a \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, b \in \left(0, \infty\right)$
TeX:
\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)
Definitions:
Fungrim symbol Notation Short description
GoldenRatio$\varphi$ The golden ratio (1.618...)
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("d774fe"),
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)))))

## Topics using this entry

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

2019-12-30 15:00:46.909060 UTC