Q16 style problems thread (2 Viewers)

[vuhung]

Thanks for the feedback.

a^3 + a^3 + b^3 >= 3a^2b
-> it is weighted AM-GM
a^3/b + a^3/b + b^2 >= 3a^2
-> ditto

"LHS and RHS have the same degree":
- They must have the same degrees
- We call it homogeneous

These techniques are tricky, olympiad-styled, not so HSC.
I see them in top selective schools' ATs but not the final HSC tests, probably you won't.

Newton's identities:
- Linked to Vieta's Formulas
- Yes, it is niche. Useful for ATs and appeared in old HSC tests, but not recent ones as what I observe.

An update uploaded here: https://github.com/vuhung16au/math-...SC-Inequalities/releases/HSC-Inequalities.pdf

 

[Flatuitous]

Thanks for the feedback.

a^3 + a^3 + b^3 >= 3a^2b
-> it is weighted AM-GM
a^3/b + a^3/b + b^2 >= 3a^2
-> ditto

"LHS and RHS have the same degree":
- They must have the same degrees
- We call it homogeneous

These techniques are tricky, olympiad-styled, not so HSC.
I see them in top selective schools' ATs but not the final HSC tests, probably you won't.

Newton's identities:
- Linked to Vieta's Formulas
- Yes, it is niche. Useful for ATs and appeared in old HSC tests, but not recent ones as what I observe.

An update uploaded here: https://github.com/vuhung16au/math-...SC-Inequalities/releases/HSC-Inequalities.pdf

Oh that is weighted AM-GM?
Sorry
I looked into it before but it looked so confusing I didn't really understand it

 

[jane1820]

jane im gna implode

what why

 

[tywebb]

View attachment 51815
View attachment 51816

here is niven's original article

Niven, Ivan (1947), "A simple proof that π is irrational" , Bulletin of the American Mathematical Society, vol. 53, no. 6, p. 509

https://www.ams.org/journals/bull/1947-53-06/S0002-9904-1947-08821-2/S0002-9904-1947-08821-2.pdf

and here is niven

 

[coolcat6778]

here is niven's original article

Niven, Ivan (1947), "A simple proof that π is irrational" , Bulletin of the American Mathematical Society, vol. 53, no. 6, p. 509

https://www.ams.org/journals/bull/1947-53-06/S0002-9904-1947-08821-2/S0002-9904-1947-08821-2.pdf

and here is niven
View attachment 51824

aw shes so adorable

 

[vuhung]

https://mwolf.pracownicy.uksw.edu.pl/Poorten_MI_195_0.pdf

Van der Poorten - who is Aussie - explained the proof of zeta(3) being irrational.

van der Poorten, Alf,
A proof that Euler missed ... Apéry's proof of the irrationality of zeta (3),
Math. Intelligencer 1 (1978/79), no. 4, 195-203.

 

[tywebb]

https://mwolf.pracownicy.uksw.edu.pl/Poorten_MI_195_0.pdf

Van der Poorten - who is Aussie - explained the proof of zeta(3) being irrationality.

van der Poorten, Alf,
A proof that Euler missed ... Apéry's proof of the irrationality of zeta (3),
Math. Intelligencer 1 (1978/79), no. 4, 195-203.

i met him. but i never met niven.

here be alf

he died in 2010

 

[tywebb]

i met him.

and u know where i met him?

50th Annual Meeting of the Australian Mathematical Society

u know who else was there?

Terence Tao

 

[Flatuitous]

and u know where i met him?

50th Annual Meeting of the Australian Mathematical Society

u know who else was there?

Terence Tao

did u meet ringo mok too

 

[justletmespeak123]

i met him. but i never met niven.

here be alf
View attachment 51825
he died in 2010

Rip. Can we trade him for Joe Biden

 

[vuhung]

thank fucking goodness I woulda necked myself right then and there

ottoowattakana,

yes, Im in y21.

 

[Flatuitous]

ottoowattakana

what does that mean

 

[justletmespeak123]

It means "nigger" in south east asian dialect

 

[vuhung]

Stop playing games, today’s challenge is literally Tetris meeting Ext 2 Math. Check out the new prob: Tetris Tile Tiling.

Why this problem is a legend:

• The Ultimate Crossover: It starts as a visual combinatorics puzzle and suddenly evolves into a Complex Numbers and Sequences boss fight. It's a brilliant look at how the syllabus connects.
• CS Source Code: Planning on studying Software Eng or Data Science? This is pure Dynamic Programming. You're basically doing the math engineers use to optimise game memory!

The Mission:

1. Build the recurrence relation, show how good your imagination is.
2. Find the complex roots using the Vieta formula.
3. Leverage the cube roots of unity to destroy the messy algebra and prove the sequence's limit.

It looks intimidating, but watching the complex terms collapse into clean real numbers is incredibly satisfying. Top-tier Q16 practice!