/sci/ - Science & Math » Thread #12612076

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How to Get Phi to Equal (1+sqrt(5))/2

Anonymous Fri 22 Jan 04:00:15 2021 No.12612076 View Reply Original Report

Quoted By: >>12612115 >>12612144

I can't figure out how to isolate Phi to one side. I'm making a serious error, and I can't figure out why.

Anonymous

Anonymous Fri 22 Jan 2021 04:19:03 No.12612115 Report

Quoted By: >>12612384

>>12612076
multiply the second equation with phi, take a long hard look and it and then hang yourself.

Anonymous

Anonymous Fri 22 Jan 2021 04:25:52 No.12612133 Report

Quoted By: >>12612201

golden ratio
$\displaystyle \begin{align*} \dfrac{a+b}{a} &= \frac{a}{b} \equiv \varphi \\ \dfrac{a+b}{a} = \dfrac{a}{a}+ \dfrac{b}{a}= 1+ \dfrac{1}{ \varphi} &= \varphi \\ \varphi + 1 &= \varphi^2 \\ \varphi^2 - \varphi - 1 &= 0 \\ \varphi &= \frac{-(-1)\pm \sqrt{(-1)^2 - 4 \cdot 1\cdot (-1)}}{2 \cdot 1} = \frac{1 \pm \sqrt{5}}{2} \\ \varphi > 0 \; \Rightarrow \; \varphi &= \frac{1 + \sqrt{5}}{2} \end{align*} $

Anonymous

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Anonymous Fri 22 Jan 2021 04:27:09 No.12612137 Report

Quoted By:

Anonymous

Anonymous Fri 22 Jan 2021 04:30:26 No.12612144 Report

Quoted By:

>>12612076
>1. Fix your handwriting
>2. Compare lines 2 and 4, you broke math
>3. Look up Golden ratio, even the wiki page walks you through the calculation

Anonymous

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Anonymous Fri 22 Jan 2021 04:58:40 No.12612201 Report

Quoted By: >>12612215 >>12612229 >>12612232 >>12612310

>>12612133
Thanks, anon. How did you go from (phi^2 - phi - 1 = 0) to (phi = (-(-1) + sqrt(((-1)^2) - 4 * 1 * (-1))) / (2 * 1))?

Anonymous

Anonymous Fri 22 Jan 2021 05:04:12 No.12612215 Report

Quoted By: >>12612229

>>12612201
ask a middle schooler, they might be able to help you out.

Anonymous

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Anonymous Fri 22 Jan 2021 05:09:24 No.12612229 Report

Quoted By: >>12612234 >>12612314

>>12612201
Easier to just use: 5^0.5 * 0.5 + 0.5 if you want to represent $\phi[\math] as a linear equation. All the other representations are simply presentations of upper and lower limits, which when it comes to <script type="math/tex">\phi[\math] is pointless to describe or bound as it is a self-enclosed loop of 3 operations, 1 integer, and 3 representations of <script type="math/tex">\frac{1}{2}[\math]. Then again I don't know what faggot professor you are trying to satisfy so suck his balls more lovingly and you'll get an A+ <script type="math/tex">\phi^-3[\math] <a href="https://boards.fireden.net/sci/thread/12612076/#12612215" class="backlink" data-function="highlight" data-backlink="true" data-board="sci" data-post="12612215">>>12612215</a> With such high rates of illiteracy and poor numerical skills I feel that high school teachers are half the problem.$

Anonymous

Anonymous Fri 22 Jan 2021 05:10:15 No.12612232 Report

Quoted By: >>12612295

>>12612201
$ \begin{align*} ax^2 + bx +c &= 0 \\ ax^2 + bx &= -c \; \; \; \; | \; \cdot 4a \\ 4a^2x^2 + 4abx &= -4ac \; \; \; \; | \; +b^2 \\ 4a^2x^2 + 4abx +b^2 &= b^2 -4ac \\ (2ax + b)^2 &= b^2 -4ac \\ 2ax + b &= \pm \sqrt{b^2 - 4ac} \\ 2ax &= -b \pm \sqrt{b^2 - 4ac} \\ \displaystyle x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{align*} $

Anonymous

Anonymous Fri 22 Jan 2021 05:11:08 No.12612234 Report

Quoted By:

>>12612229
the curse of the inverted slash for /math claims another victim

Anonymous

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Anonymous Fri 22 Jan 2021 05:43:06 No.12612295 Report

Quoted By:

>>12612232
Thanks, anon. I remember watching this video that features a geometric proof for the quadratic formula.

https://youtu.be/N-KXStupwsc?t=583

Anonymous

Anonymous Fri 22 Jan 2021 05:48:04 No.12612310 Report

Quoted By:

>>12612201
>How did you go from (phi^2 - phi - 1 = 0) to (phi = (-(-1) + sqrt(((-1)^2) - 4 * 1 * (-1))) / (2 * 1))?

Isn't it obvious for you that that is just a second order equation? Maybe if you change phi by "x" it should be clear to you.

Anonymous

Anonymous Fri 22 Jan 2021 05:51:20 No.12612314 Report

Quoted By:

>>12612229
>\math

XML $\neq \LaTeX$

Anonymous

Anonymous Fri 22 Jan 2021 06:23:35 No.12612384 Report

Quoted By:

>>12612115
kek

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