NOTE: for those who cant read the below equations (they aren't rendered) you can follow this link to see: mathb.in/38381

Here you go a full derivation from the math equations you started with to the one I provided you several times...

axioms (given by you, agreed by physicist):

\[E = {m}_{rel} \cdot {C}^{2}\]

\[{E}^{2} = {p}^{2} \cdot {C}^{2} + {{m}_{rest}}^{2} \cdot {C}^{4}\]

De Broglie's Equation for the momentum of a photon:

\[p = \frac{h}{\lambda}\]

Formula to convert wavelength \(\lambda\) into a frequency:

\[\lambda = \frac{C}{f}\]

Simplify given axioms:

\[{({m}_{rel} \cdot {C}^{2})}^{2} = {p}^{2} \cdot {C}^{2} + {0}^{2} \cdot {C}^{4}\]

\[{{m}_{rel}}^{2} \cdot {C}^{4} = {p}^{2} \cdot {C}^{2}\]

\[{{m}_{rel}}^{2} = \frac{{p}^{2} \cdot {C}^{2}}{{C}^{4}}\]

\[{{m}_{rel}}^{2} = \frac{{p}^{2}}{{C}^{2}}\]

\[{m}_{rel} = \sqrt{\frac{{p}^{2}}{{C}^{2}}}\]

then use de broglie's equation for the momentum...

\[{m}_{rel} = \sqrt{\frac{{(\frac{h}{\lambda})}^{2}}{{C}^{2}}}\]

\[{m}_{rel} = \sqrt{\frac{\frac{{h}^{2}}{{\lambda}^{2}}}{{C}^{2}}}\]

\[{m}_{rel} = \sqrt{\frac{{h}^{2}}{{C}^{2} \cdot {\lambda}^{2}}}\]

Now convert wavelength to frequency...

\[{m}_{rel} = \sqrt{\frac{{h}^{2}}{{C}^{2} \cdot {(\frac{C}{f})}^{2}}}\]

\[{m}_{rel} = \sqrt{\frac{{h}^{2}}{{C}^{2} \cdot \frac{C^2}{f^2}}}\]

\[{m}_{rel} = \sqrt{\frac{{h}^{2}}{\frac{C^4}{f^2}}}\]

\[{m}_{rel} = \sqrt{{h}^{2} \cdot \frac{f^2}{C^4}}\]

\[{m}_{rel} = \sqrt{\frac{{h}^{2} \cdot f^2}{C^4}}\]

and bam you arrive at the equation for the relativistic mass of a photon.

\[{m}_{rel} = \frac{h \cdot f}{c^2} \]


friends don't ask friends to install proprietary software

Did we seriously just get our first "vaccines cause autism" post on QOTO... sad day. Lets hope this doesnt become a trend and we keep having real science here.

long_running_command ; [Ctrl-Z] ; bg ; disown ; screen ; reptyr $( pidof long_running_command ) # Suspend and reattach a process within screen.

These are the first 100,000 complex points in a sequence where each point is a root of a quadratic equation. Start with x^2 + x + 1 = 0 and use its roots as the coefficients for the next polynomial.


Start with 82 and go backwards to 1

8281807978777675747372717069686 7666564636261605958575655545352 5150494847464544434241403938373 6353433323130292827262524232221 2019181716151413121110987654321

...this number is prime!

A friend just had a brilliant idea, though a bit odd, for the meat issue... Lizard tails. They pop off with no health risks to the animal, and they grow back. infinite meat source, no killing.

Glad to see players are getting good at The Copied Factory, had a couple near perfect runs this weekend!

I feel like we need a bot to post ASSIST and ACM journal papers too. I love the arXiv bots we have so much that it makes sense to expand that a bit, considering we are a STEM instance.

Don't just teach your students to read.
โ€ข Teach them to question what they read, what they study.
โ€ข Teach them to doubt.
โ€ข Teach them to think.
โ€ข Teach them to make mistakes and learn from them.
โ€ข Teach them how to understand something.
โ€ข Teach them how to teach others.

Credits: @proffeynman@twitter.com

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