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

[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.

 

[WWGD]

One of my favorites: For n>2 , every number 1 less than a square is composite:

$n^2 -1 =(n+1)(n-1)$. You get the actual factorization for free.

Example: $899=900-1 =(30+1)(30-1)=31 *29$

 

[strangerep]

[...] TV quiz show called Countdown [...]

I love the "8 out of 10 cats" version of that show. At first I thought Rachel Riley must be getting fed the formulas via an ear piece, but gradually realized she is a genuine arithmetic savant -- proving once again that life is deeply unfair, since she is also drop-dead good looking.

(Jon Richardson is also pretty incredible in the word part of the game). After I'd watched several episodes of the show I became pretty depressed at how crap I am...

The Australia version "Celebrity Letters and Numbers" features Lily Serna in Rachel's role. She's also a LOT quicker than me at finding difficult formulas mentally.

 

[Tom.G]

My doc wants to staple an afterbirth onto my eye.

The attachment method is different but, here in the US after a chemical burn damages the cornea an afterbirth (placenta) is applied to promote smooth healing and improve vision somewhat during healing.

No mechanical attachment is needed. It is like applying a very thin plastic film to wet glass, it stays put.

Cheers,
Tom

 

[Ibix]

I love the "8 out of 10 cats" version of that show. At first I thought Rachel Riley must be getting fed the formulas via an ear piece, but gradually realized she is a genuine arithmetic savant -- proving once again that life is deeply unfair, since she is also drop-dead good looking.

There's a clip on YouTube where somebody (Lee Mack, I think) asked her "how she got like that" when she was kicking herself for solving a problem one way and only noticing afterwards that she could construct it in a more elegant way. She just said she's done it a lot. And if you think about it, the regular Countdown is on five days a week and she's been co-hosting for years now, which is a lot of repetition just on screen. Practice makes perfect, I guess.

 

[dlgoff]

Only problem with living in Kansas are the thunderstorms. Power loss=No PF

 

[strangerep]

(Lee Mack, I think) asked her "how she got like that"

No doubt she was too polite to reply "Because I wasn't born as thick-headed as you."

I guess she (and Suzie Dent) must be getting quite a good salary to put up with the frequent crap they cop from Jimmy Carr.

 

[Char. Limit]

What if I popped up here again? Wouldn't that be weird?

 

[pinball1970]

What if I popped up here again? Wouldn't that be weird?

SAS Commando?
I missed out on that one, Welcome back!

 

[Char. Limit]

SAS Commando?
I missed out on that one, Welcome back!

Thank you! And thanks for the welcome from @WWGD and @Borg as well. It's been a good while but I'm glad to see you're doing well.

 

[Borg]

It's been a good while

I looked at your last post. It was 6 years ago. Going to hang out for a while?