Christian Lawson-Perfect @christianp

279 posts85 participants2 posts today

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 32m

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hello,
The hectoc of the hour is:

634792

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. Please use CW "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 1h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Greetings fellow humans,
The hectoc of the hour is:

752877

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 2h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hello everyone,
Your hourly hectoc is here:

766361

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 3h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Dear mental calculators,
Your hourly hectoc is here:

866336

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 4h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hello math fans,
The hectoc of the hour is:

738884

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 5h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hello everyone,
Here is a new hectoc challenge for you:

266578

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 6h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hello,
The hectoc of the hour is:

265354

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 7h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hi!
Your hourly hectoc is here:

432118

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 8h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hi!
Here is a new hectoc challenge for you:

222429

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Paysages Mathématiques** @paysmaths · 9h

Paysages Mathématiques @paysmaths

"Sans un minimum d’ouverture à la beauté des choses, j’aurais été bien incapable de "fonctionner" comme mathématicien, même à un régime des plus modestes – et je doute que quiconque puisse faire travail utile en mathématiques, s’il ne reste vivant en lui, tant soit peu, ce sens de la beauté." – Alexandre Grothendieck (1928-2014)
#citation #mathématiques #maths #math

Portrait photographique d'Alexandre Grothendieck, et une citation : "Sans un minimum d’ouverture à la beauté des choses, j’aurais été bien incapable de "fonctionner" comme mathématicien, même à un régime des plus modestes – et je doute que quiconque puisse faire travail utile en mathématiques, s’il ne reste vivant en lui, tant soit peu, ce sens de la beauté."

**Paysages Mathématiques** @paysmaths · 9h

Paysages Mathématiques @paysmaths

"Without a minimum of openness to the beauty of things, I would have been quite unable to "function" as a mathematician, even at a modest level – and I doubt that anyone could do useful work in mathematics if that sense of beauty didn't remain alive in them, at least to some extent." – Alexandre Grothendieck (1928-2014)
#quote #mathematics #math #maths

Photographic portrait of Alexandre Grothendieck, and a quote : "Without a minimum of openness to the beauty of things, I would have been quite unable to "function" as a mathematician, even at a modest level – and I doubt that anyone could do useful work in mathematics if that sense of beauty didn't remain alive in them, at least to some extent."

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 9h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hello everyone,
Your hourly hectoc is here:

596732

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Hacker News** @h4ckernews@mastodon.social · 10h

10h

Hacker News @h4ckernews@mastodon.social

PlanetMath

https://planetmath.org/

#HackerNews #PlanetMath #Math

**Hourly Hectoc Bot** @hourlyhectoc@mastodon.seism0saurus.de · 10h

10h

Hourly Hectoc Bot @hourlyhectoc@mastodon.seism0saurus.de

Hello math fans,
A new hectoc for you:

437444

Have fun! Your hourly hectoc bot
by @seism0saurus

hectoc.seism0saurus.deHectoc

#math #mentalcalculator #hectoc

**Prof. Bholanath Dutta** @break_the_silos@mastodon.social · 11h

11h

Prof. Bholanath Dutta @break_the_silos@mastodon.social

Can you SOLVE this ? #math

**Jacques Timmermans** @JacquesTimmermans · 11h

11h

Jacques Timmermans @JacquesTimmermans

☆ Π MTH ~Ci~✧⁰¹⁰¹ Π∞ßτ З²⁶⁶ ⁰⁰כ

Innocent question ...

In the expression

$\sqrt{r - \sqrt{m}} + \sqrt{r + \sqrt{m}} = n$
When are m, r and n integers?

Squaring
${(\sqrt{r - \sqrt{m}} + \sqrt{r + \sqrt{m}})}^{2} = n^{2}$
We have
$\begin{matrix} {(\sqrt{r - \sqrt{m}})}^{2} + \\ 2 \sqrt{r - \sqrt{m}} \sqrt{r + \sqrt{m}} + \\ {(\sqrt{r + \sqrt{m}})}^{2} \\ = n^{2} \end{matrix}$
That is
$\begin{matrix} r - \sqrt{m} + \\ 2 \sqrt{r^{2} - {(\sqrt{m})}^{2}} + \\ r + \sqrt{m} \\ = n^{2} \end{matrix}$
Or
$\begin{matrix} 2 r + 2 \sqrt{r^{2} - m} = n^{2} \end{matrix}$
Finally
$n = \sqrt{2 r + 2 \sqrt{r^{2} - m}}$

The expression was studied for $m, r \in [0, 100]$ using Python code ...

《

import math

def SimplRad():
MAX = 100
for r in range(0,MAX):
for m in range(0,MAX):
if (r**2 >= m):
n = math.sqrt(2*r + 2* math.sqrt(r**2 - m))
if (n == int(n)):
print(m,r,n)

SimplRad()

》

From which we get

$\begin{matrix} m & r & n \\ 0 & 0 & 0 \\ 0 & 1 & 2 \\ 4 & 2 & 2 \\ 0 & 4 & 4 \\ 16 & 5 & 4 \\ 32 & 6 & 4 \\ 48 & 7 & 4 \\ 64 & 8 & 4 \\ 0 & 9 & 6 \\ 36 & 10 & 6 \\ 72 & 11 & 6 \\ 0 & 16 & 8 \\ 64 & 17 & 8 \\ 0 & 25 & 10 \\ 0 & 36 & 12 \\ 0 & 49 & 14 \\ 0 & 64 & 16 \\ 0 & 81 & 18 \end{matrix}$
Just like the beautiful result
$\sqrt{11 - \sqrt{72}} + \sqrt{11 + \sqrt{72}} = 6$
We conjecture that if $n \in N$ is odd there are no $m, r \in N$ such that $\sqrt{r - \sqrt{m}} + \sqrt{r + \sqrt{m}} = n$