(Can I be excused for missing it at the time?)

It’s that wonderful time of year where you get free online talks about inclusive design for a whole 24 hours courtesy of Inclusive Design 24.

In two days: 23rd September, don’t miss out!

solution

So my question is: was this set up so that the golden ratio ϕ=(1+√5)/2 would turn up, or could you cook up a similar puzzle without it?

solution

...

\[\left(\frac{5}{3}\right)^x = \frac{1 \pm \sqrt{5}}{2}\] (quadratic formula)

\[\left(\frac{5}{3}\right)^x = \frac{1 + \sqrt{5}}{2}\] (only one root is real)

\[x \ln \left(\frac{5}{3}\right) = \ln\left(\frac{1 + \sqrt{5}}{2}\right)\] (take logs)

\[x \left(\ln5 - \ln3\right) = \ln\left(1 + \sqrt{5}\right) - \ln2\]

\[x = \frac{\ln\left(1 + \sqrt{5}\right) - \ln2}{\ln5 - \ln3}\]

solution

Here's my working:

Want to solve for \(x\):

\[ 9^x + 15^x = 25^x \]

First guess: it's a little bit less than \(1\):

\[\begin{eqnarray*}

9^0 + 15^0 &=& 2 &>& 1 = 25^0 \\

9^1 + 15^1 &=& 24 &<& 25 = 25^1

\end{eqnarray*}\]

Do some rearranging:

\[9^x+15^x=25^x\]

\[1+ \left(\frac{5}{3}\right)^x = \left(\frac{25}{9}\right)^x\] (divide by \(9^x\))

\[\left(\frac{25}{9}\right)^x - \left(\frac{5}{3}\right)^x - 1 = 0\]

\[\left(\frac{5}{3}\right)^{2x} - \left(\frac{5}{3}\right)^x - 1 = 0\]

...

@esoterica Multiplicative/product calculus, as described by this preprint, is also described nicely by some of the books hosted on this site: https://sites.google.com/site/nonnewtoniancalculus/ and this other preprint: http://math.ups.edu/~mspivey/ProdCalc.pdf .

Here's a link: https://cuttle.xyz/@christianlp/Tiling-qXUhQ5MkCnAL

RT @AngelikiKoutso1@twitter.com

An amazing discovery today during my random stroll (someplace in Greece, in a secret location)! As I took a shortcut through a tiny street, I was thrilled to see that someone had filled the place with beautifully drawn Geometry theorems! [1/9]

🐦🔗: https://twitter.com/AngelikiKoutso1/status/1428795625974468623

To take time off, I have to fill in an "annual leave request form". It's a web form hand-coded by local IT, because nobody else does this, so we need a bespoke tool, of course?

Anyway, the form asks for "hours required". Turns out the label is rewritten to "days required" in the email the office staff get, but the number stays the same.

I only discovered this because the person who normally handles it is on leave herself. So she'd just been ignoring this for years!

What's my pattern?

1,2,3,6,4,5,12,10,8,7,...

(not a #LullabySequence, or at least I haven't done the maths to make it easy to chant without stopping to think yet)

- Homepage
- http://somethingorotherwhatever.com

- Location
- Newcastle upon Tyne, UK

- Pronouns
- he/him

- Favourite number
- 3435

Admin

Mathematician, koala fan, mathstodon.xyz admin,

⅓ of https://aperiodical.com. He/him

Joined Apr 2017