Eternity In An Hour

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@gerryiles3925 12 сағат бұрын

You can use the same "flipping over a copy" argument, but with the 4 shaded segments, you used for B for the last one to show it must be less than half of the circle.

@eternity_hour 11 сағат бұрын

You're right, I didn't fully my own advice and use the same trick. Thanks for pointing that out

@normanklein3155 6 сағат бұрын

This seems to be one of those questions, where it's just not really worth knowing the answer to it. As the answer doesn't really lead to any greater knowledge, except for answering stupid questions on tests.

@kurzackd 3 ай бұрын

That's phi - 1 i.e. the golden ration ( φ = 1.618... ) MINUS 1 (ONE) !! :) .

@eternity_hour 3 ай бұрын

The very same

@vladislavguliy2407 3 ай бұрын

please test GPT-4o and Claude 3.5 Sonnet, they are 15-30% smarter than GPT-4 in all tasks (in complex mathematical ones, maybe much better, maybe not - it's still a mystery). And use one-shot, few-shot methods (1...n demonstration with examples) for more correct answers

@eternity_hour 3 ай бұрын

Thanks for the suggestions - I've used it so much more for maths these days and you're right that it's still a mystery: some simple problems it just cannot respond to properly even when worded simply, but some more vague complex questions it manages to complete well

@dkloke 3 ай бұрын

Adding 1 gives us a rational coefficient to measure the irrational one against, then repeated squaring refines the ratio of the coefficients, very satisfying! It's not a sieve, could it be called a wringer?

@eternity_hour 3 ай бұрын

thanks for the comment! Yes I think wringer is a great name indeed. did you attempt the problems at the end to develop ‘wringers’ for other irrationals? An even further extension is to work on making rational approximations for ‘doubly irrational’ numbers like sqrt(1+sqrt(2))

@benjaminlukwiya 3 ай бұрын

For the 1st question, why did you complete the square? (Isn't that just for finding the turning point).

@eternity_hour 3 ай бұрын

Yes but the turning point of a negative quadratic is also it's maximum as squares of real numbers have a minimum of zero. Other functions don't have simple algebraic properties like this that allow you to find their maxima and minima, which is why you learn new techniques at A-Level

@haidara77 4 ай бұрын

hey man long time no see, i had universty exams latly and didnt had a chance to revist the channel. I love those kind of problems where you feel it might happen in a real world scenario, unlike other math problems where you feel you are just learning for grades sake. the way i solve it is by writing all posible outcomes, so i got: if the 3 variables are positves we will get 1+1+1+1=4 if the 3 variables are negatives we will get -1-1-1-1=-4 if 2 variables are negatives we will get -1-1+1+1=0 if 2 variables are positves we will get 1+1-1-1=0 and then i got stuck for 7 minutes wondering why i got -4 and 4, but then i remmbered that a+b+c=0 which means that we cant have 0 if all nummbers are postive/negative. so the answer cant be the first two options which leaves us with 0

@eternity_hour 4 ай бұрын

Thanks for your comment and your revisit. If you want to take this problem to the next level, see what happens if you increase the number of variables to 4,5 and then n - can you spot any general patterns?

@amaay1498 4 ай бұрын

Hi just to want to test your knowledge, can you solve this question: If f(x) is a differentiable function and g(x) is a double differentiable function such that If(x) | ≤ 1 and f'(x) = g(x). If f^2(0) + g^2(0) = 9. Prove that there exists some C € (-3, 3) such thatg(c). g"'(c) < 0.

@eternity_hour 4 ай бұрын

If f(x) = sin(3x), g(x) = 3cos(3x), g”(x) = -27cos(3x), if c = 0, g”(x) = -27, which is less than zero.

@tahmidhassan1088 4 ай бұрын

i hope edexcel dont take inspiration for gcse paper 3....

@eternity_hour 4 ай бұрын

Pretty unlikely, though part of me wishes that each paper ended with a bonus question like this one

@danixx2323 4 ай бұрын

Thank you so much! How would you work out the second question using a formula?

@eternity_hour 4 ай бұрын

When I said formula, I should have said algorithm. There are several and are listed here: en.wikipedia.org/wiki/Chinese_remainder_theorem It’s a very powerful tool and result which extends far beyond integers

@S1NGH1838 4 ай бұрын

Great vid! Shouldn’t the answer for the first one be: -_/2 + _/(2+_/2) _________________ 2

@voodoocurry2762 4 ай бұрын

That’s what I was thinking how he got_/ (2+2_/2)

@eternity_hour 4 ай бұрын

let me check, thanks for looking

@eternity_hour 4 ай бұрын

isn’t this what I wrote?

@S1NGH1838 4 ай бұрын

@@eternity_hour I don’t believe so as you wrote: 2+2_/2 not 2+_/2

@eternity_hour 4 ай бұрын

I see now. when you multiply by root2, inside the first root this appears as a 2. So sqrt(1+sqrt(2)) * sqrt(2) = sqrt(2*(1+sqrt(2)) = sqrt(2+ 2sqrt(2)) www.wolframalpha.com/input?i=sqrt%281%2Bsqrt2%29+*+sqrt%282%29

@pulselunat389 4 ай бұрын

can someone explain the 1-root(1+root2) * -root2 = root(2=2root2) please

@eternity_hour 4 ай бұрын

You have to rationalise the denominator twice, but there is some nice simplification.

@surfaceten510n 4 ай бұрын

@alexdutton4937 4 ай бұрын

Fanx

@omg_look_behind_you 4 ай бұрын

62, 70, 77, 91, 101, 103, 107, 115, etc... You add the digits of a number to itself to get the next number. Also FIRST!

@eternity_hour 4 ай бұрын

Nice work! Did you have a go at the other questions at the end? Also, what is up with your username?

@CrazyLobster-b9t 24 күн бұрын

Next Is 122 then 127,137

@gamerbacondude9816 5 ай бұрын

Please can you do a sum like 2^2005 x 5^2005

@eternity_hour 5 ай бұрын

That would be 1 followed by 2005 zeros.

@gamerbacondude9816 5 ай бұрын

Well done bro, I really learnt something from this video

@eternity_hour 5 ай бұрын

Glad to hear that

@unknown_kingzzz4120 5 ай бұрын

need the 8/9 so i can do further for A-level

@eternity_hour 5 ай бұрын

Good luck, further maths is a great A-level that will push your maths to 1st year degree level in some places so be prepared!

@unknown_kingzzz4120 5 ай бұрын

@@eternity_hour im not going to lie edexcel ruined me hard today i might have scraped an 8 so i gotta score high in paper 2 and 3 to guarantee further for a-level

@JullliaV 5 ай бұрын

Thx!

@eternity_hour 5 ай бұрын

glad I could help

@RobertLeversyt 5 ай бұрын

I am working hard for this 9 thanks for this video 🎉

@eternity_hour 5 ай бұрын

You got this!

@riannapilled 5 ай бұрын

i am getting this fucking 9 man

@eternity_hour 5 ай бұрын

Good luck, with that attitude you can’t go wrong!

@ShauryaPandey-mj5tz 5 ай бұрын

Thank you so much for your video! At the moment, I'm getting about 70-ish marks in my Maths papers so i don't know if I am someone suited for this video. However, I really enjoyed giving your question a try (I got it wrong the first time) and I was hoping to see more of them. The link in your description doesn't seem to work for the worksheets. Do you mind posting through another link so that I could have a look? Thank you so much and please keep on posting these videos - hoping to keep my brain occupied in the 3 months I'll have after my GCSEs!

@eternity_hour 5 ай бұрын

And thanks for your comment! I've fixed the link now, much appreciated that you pointed that out. www.alexdutton.me/store/p/gcse-maths-extra-hard-problems Keep subscribed and you'll see I post a new maths challenge question every Monday.

@ShauryaPandey-mj5tz 5 ай бұрын

Sorry to add on, after looking at the second question I was trying to find a way using algebra to find the answer. I know you mentioned the existence of an equation which can help find the answer. Could you please tell me what it is too? I don't prefer the current method since I just feel like it's 'brute force' to find the answer. Thanks!

@eternity_hour 5 ай бұрын

en.wikipedia.org/wiki/Chinese_remainder_theorem

@ShauryaPandey-mj5tz 5 ай бұрын

@@eternity_hour Cheers!

@IvayloHristakiev 5 ай бұрын

The thumbnail has a different problem

@eternity_hour 5 ай бұрын

It was a little hard to get the whole question into a thumbnail, and it is much simpler. Sorry for any confusion

@mysteriouspikachuman 5 ай бұрын

🤑🤑🤑 (i forgot how to do this)

@eternity_hour 5 ай бұрын

Thanks buddy - this is great practice material for your algebra - look at the material at the end!

@manpreetbhandal8255 6 ай бұрын

Thank you, this video helped a lot

@eternity_hour 6 ай бұрын

Glad to hear it! Making solution videos is all I have time for these days so I’ll try to do a whole Gauss paper next.

@mysteriouspikachuman 7 ай бұрын

ANOTHER BANGER OF A VIDEO

@eternity_hour 7 ай бұрын

Out of my fans, you are truly one of them.

@NorbertKasko 7 ай бұрын

It can't do the hyperfactorial function. In 2024! It also struggled with some normal very large factorials. It should've compare them. The comparison was wrong. It said about the smaller number that it's bigger.

@eternity_hour 7 ай бұрын

Still a lot of limitation - correct.

@DetPrep 7 ай бұрын

A week ago I asked something related to math, ChatGpt opened Phyton and used it to get precise calculation with top quality self prompting, that was Smart from ChatGpt, I have to admit it

@eternity_hour 7 ай бұрын

These days it's much better but you're right it has to outsource.

@JenChan 7 ай бұрын

I think this is a great video because it's taught me something I had no idea at all about before! 🤩

@eternity_hour 7 ай бұрын

I'm glad to hear it, thanks for your support kind stranger

@mysteriouspikachuman 8 ай бұрын

Another great video thanks m80 😀

@eternity_hour 8 ай бұрын

Thanks a bunch o buddy o pal

@haidara77 8 ай бұрын

Nice problem i learned something new today, but i do miss the old profile picture you had

@eternity_hour 8 ай бұрын

One day it might come back!

@mysteriouspikachuman 8 ай бұрын

‘babe, new eternity in an hour video just dropped’

@eternity_hour 8 ай бұрын

Thanks bro - ever think of entering the amc 8 next year?

@ArsenalCazorla19 8 ай бұрын

hi. do you know if you could send a picture of your task, and then they could answer it?

@eternity_hour 8 ай бұрын

In some cases it can read text from an image, but it can struggle with anything actually visual like a geometry problem without accompanying text.

@julianaoren8024 9 ай бұрын

😂 *Promo sm*

@eternity_hour 9 ай бұрын

Always with this promo sm spam

@AlexanderDuttonMusic 9 ай бұрын

🎉

@eternity_hour 9 ай бұрын

Thanks

@atlasboratok9954 9 ай бұрын

49/98 same thing

@eternity_hour 9 ай бұрын

Yes, there an infinite number of these, beyond trivial extensions like 490/980 to use your example. I have a post up with a graph showing the distribution of digit-cancelling fractions and a longer video.

@atlasboratok9954 9 ай бұрын

@eternity_hour nerd

@369solomonsrequiem 10 ай бұрын

I would like you to test wolfram alpha plug in for chat gpt 4, I hear good things from it.

@jagdeeprana5802 10 ай бұрын

👍

@eternity_hour 10 ай бұрын

Thanks! Don't forget to subscribe to catch the next one

@devakritbagchi2787 10 ай бұрын

You mean, chatgpt 4.0 behaves more like an exam student. When it realizes that it's going to fail, it just does it wrong, but DOES do it. This's what happens when you're getting your training data from thus, gansters, cheating students and Mr. Bean.

@eternity_hour 10 ай бұрын

Do we know where chat GPT is supposed to have learned maths from?

@devakritbagchi2787 10 ай бұрын

@@eternity_hour Well I was being sarcastic but it's not a complete falsie. Reading such response (apart from credible sources like online published books) is important to make it more human.

@AlexanderDuttonMusic 11 ай бұрын

Great stuff - keep it up looking forward to more of these.

@eternity_hour 11 ай бұрын

Thanks, will do! More to come each week

@writerightmathnation9481 11 ай бұрын

Early on, he said the denominator was 2334 and the numerator was 12387, but showing in the screen was a fraction whose numerator is 2334 and whose denominator is 12837. Strange.

@eternity_hour 11 ай бұрын

you caught me, thanks for pointing this out!

@writerightmathnation9481 11 ай бұрын

@@eternity_hour You’re quite welcome.

@jahbini Жыл бұрын

Tanalizing

@eternity_hour Жыл бұрын

Cromulent

@jahbini 10 ай бұрын

I hate spell check: where was it when I needed it?@@eternity_hour