What is the newest installment of 'Random Thoughts' on Physics Forums?

[WWGD]

Seems, according to The Economist, Russia has denied IP rights to products coming from " Enemy States ".

 

[fresh_42]

Now Putin likens himself to Peter the Great.

He had the chance. Peter the Great opened Russia to Europe, and science and progress were on his agenda. All of that could have been Putin's merits, too. However, he has chosen to be like Stalin.

 

[Astronuc]

Putin undermined his own rationale for invading Ukraine, admitting that the war is to expand Russian territory
https://www.businessinsider.com/putin-says-ukraine-war-seize-land-russia-undermines-rationale-2022-6

Russian President Vladimir Putin said publicly for the first time Thursday that his invasion of Ukraine is about expanding Russian territory, as Western leaders have long maintained.

Speaking to students Thursday after visiting an exhibition about Peter the Great, Russia's first emperor credited with making the country a major power in the early 18th century, Putin compared himself to the ruler and said they were both destined to expand Russia.

As well as seizing territory in a 21-year war with Sweden in the late 17th century, Peter also captured the territory of Azov from Crimean Tatars, who were aligned with Turkey, in 1696, and seized territory on the Caspian Sea from Persia in 1723.

Veiled warning to neighboring states?

In a tweet Friday, Mykhailo Podolyak, an advisor to Ukrainian President Volodymyr Zelenskyy, said Putin's comments prove his "contrived pretexts of people's genocide" in Ukraine were false and demanded "immediate de-imperialization" of Russia.

From The Hill - Putin compares self to Peter the Great, says he is taking back Russian lands
https://thehill.com/news/3518666-pu...e-great-says-he-is-taking-back-russian-lands/

 

[Bystander]

Anyone have trouble distinguishing Eugene Roche, https://www.google.com/search?q=eug...12j0i512l3.20284j0j7&sourceid=chrome&ie=UTF-8 from M. Emmet Walsh https://www.google.com/search?gs_ss...i57j0i30l6.11264j0j7&sourceid=chrome&ie=UTF-8

 

[Borg]

Gmail cut off pop access to my Outlook while I was on vacation. I *only* had to spend 3 hours changing over to IMAP and getting the settings back to something close to what they were previously.

 

[Astronuc]

https://www.msn.com/en-us/money/other/the-e-u-stands-firmly-behind-ukraine-s-bid-to-receive-eu-candidate-status/ Rather late.

Meanwhile - Yale historian Timothy Snyder says Putin is 'preparing to starve much of the developing world' in order to win Russia's war in Ukraine. Of course, he is, and Putin is willing to murder as many people as necessary to take control of Ukraine.
https://www.msn.com/en-us/news/world/putin-is-preparing-to-starve-much-of-the-developing-world-in-order-to-win-russias-war-in-ukraine-yale-historian-says/

 

[fresh_42]

Just found another strange immigrant: vogelfrei. And to whom it may concern. Well, I guess I am vogelfrei on PF. Just use the report button to avoid collisions with our rules. Happy insulting!

 

[WWGD]

Maybe Foo Fighter's "I'll Stick Around" qualifies as " Angry Rock" ?

 

[Mayhem]

Mental math trick I realized too late in life.

(n-b)a = na-ab

E.g. 99*13 is hard to multiply mentally, but 100*13-13 isn't, where n = 100, b = 1, and a = 13.

 

[fresh_42]

Mental math trick I realized too late in life.

(n-b)a = na-ab

E.g. 99*13 is hard to multiply mentally, but 100*13-13 isn't, where n = 100, b = 1, and a = 13.

Similar with $n\cdot (n+2).$ It is $((n+1)-1)\cdot ((n+1)+1)=(n+1)^2-1.$
E.g. $17\cdot 19$ is hard, but $18^2-1$ is not; at least if you know some squares by heart.

 

[pinball1970]

Similar with $n\cdot (n+2).$ It is $((n+1)-1)\cdot ((n+1)+1)=(n+1)^2-1.$
E.g. $17\cdot 19$ is hard, but $18^2-1$ is not; at least if you know some squares by heart.

is there a short cut for squares?

 

[Jonathan Scott]

is there a short cut for squares?

You can factorise the number being squared, so for example $18^2$ is $9^2 \times 2^2$.

 

[DrGreg]

You can factorise the number being squared, so for example $18^2$ is $9^2 \times 2^2$.

In this example, you could treat it as $$(20 - 2)^2 = 20^2 - 2 \times 20 \times 2 + 2^2 = 400 - 80 + 4 = 324 = 18^2$$

EDIT: typo corrected, thanks to Ibix (below)
EDIT: 2nd typo corrected, thanks to pinball1970 (further below). Not quite as easy as I first claimed, how embarassing! Conclusion: I'm better at algebra than numeric calculation.

 

[pinball1970]

You can factorise the number being squared, so for example $18^2$ is $9^2 \times 2^2$.

That works

In this example, you could treat it as $(20 - 2)^2 = 20^2 - 2 \times 20 + 1$

I think I got my PEDMAS wrong

 

[Ibix]

In this example, you could treat it as $(20 - 2)^2 = 20^2 - 2 \times 20 + 1$

There's a typo here - there should be a 4 at the end there, not 1.

 

[DrGreg]

Mental math trick I realized too late in life.

(n-b)a = na-ab

E.g. 99*13 is hard to multiply mentally, but 100*13-13 isn't, where n = 100, b = 1, and a = 13.

In the UK there is a long-running and well-known TV quiz show called Countdown which includes a game where the contestants are given 6 random integers and a random target. The goal is to combine some or all of the six numbers using addition, subtraction, multiplication and division to obtain the target, and all within 30 seconds. The trick above is one way to reach a target quickly as it allows you to effectively use the same number twice.

That is, if you declare your calculation as $na-ab$ you are deemed to have used $a$ twice, which isn't allowed (unless the 6 random integers included $a$ twice). But f you declare your calculation as $(n-b)a$ you are deemed to have used $a$ only once.

 

[DrGreg]

In this example, you could treat it as $(20 - 2)^2 = 20^2 - 2 \times 20 + 1$

There's a typo here - there should be a 4 at the end there, not 1.

Silly me! Original post now corrected.

 

[fresh_42]

is there a short cut for squares?

not that I knew, but I learned them up to 20 and multiples of 5 are easy, powers of 2 known.

 

[pinball1970]

Silly me! Original post now corrected.

So that is definitely right?

 

[pinball1970]

Silly me! Original post now corrected.

Not changing both to 2sq? Take 80 off then 4 back?

 

[DrGreg]

Not changing both to 2sq? Take 80 off then 4 back?

Yes you are right, I really messed that up. I must be getting old faster than I thought.

 

[fresh_42]

My doc wants to staple an afterbirth onto my eye.

 

[pinball1970]

My doc wants to staple an afterbirth onto my eye.

That's nuts, just googled it. Hope it works out

 

[pinball1970]

Yes you are right, I really messed that up. I must be getting old faster than I thought.

I'm just glad! thought I was going nuts!

 

[fresh_42]

That's nuts, just googled it. Hope it works out

Thank you.

And I learned that to staple is by far not what I wanted to express. The German word tackern fits much better.

 

[WWGD]

is there a short cut for squares?

I'm told I'm kind of a square ;). This is often helpful:

Use that $a^2-b^2=(a-b)(a+b)$
So that:
$a^2=(a-b)(a+b)+b^2$ (1)

So you look for convenient choices for b to simplify the multiplication.

Example. Compute $988^2$

Here you can choose $b=12$.Then , in (1) above, we get:

$988^2=(988-12)(988+12)+12^2$ =
$(976)(1000)+ 12^2=976144$

It tends to impress people. But its often the people who are impressed when you come up with the answer to $1000^2$

 

[fresh_42]

What we call the third binomial formula at school (a+b)(a-b) here is the unsung hero of all binomial theorems in my opinion. It is useful in so many places that it surprised me that I haven't found an English name for it.

 

[WWGD]

What we call the third binomial formula at school (a+b)(a-b) here is the unsung hero of all binomial theorems in my opinion. It is useful in so many places that it surprised me that I haven't found an English name for it.

I've heard it called a ' workhorse'.

 

[fresh_42]

I've heard it called a ' workhorse'.

It is, indeed!

 

[pinball1970]

It is, indeed!

Only a mathematician would say that.