Search found 194 matches
- Thu May 27, 2021 10:17 am
- Forum: Site Support
- Topic: Test
- Replies: 0
- Views: 10073
Test
In geometry, the Conway triangle notation, named after John Horton Conway, allows trigonometric functions of a triangle to be managed algebraically. Given a reference triangle whose sides are a, b and c and whose corresponding internal angles are A, B, and C then the Conway triangle notation is simp...
- Wed May 26, 2021 2:26 pm
- Forum: College / University Level
- Topic: Maybe not as hard as you see
- Replies: 8
- Views: 22962
Re: Maybe not as hard as you see
BUMPTY BUMPTY BUMP Why no body trying this beautiful problem?
- Tue May 25, 2021 10:36 pm
- Forum: College / University Level
- Topic: Maybe not as hard as you see
- Replies: 8
- Views: 22962
Re: Maybe not as hard as you see
Prove that any closed loop is inscribed in a square .(It is not the unsolved topology problem rather a brain teaser) Disclaimer: I don't know how to prove it formally but the intuitive proof(key) is enough. Hint: It is easy to prove that every closed loop is inscribed in a rectangle then try to mes...
- Tue May 25, 2021 9:50 pm
- Forum: Number Theory
- Topic: Hard Diophantine (maybe)
- Replies: 7
- Views: 11487
Re: Hard Diophantine (maybe)
pythagorean triple? Yeap.(But not so easy to prove).If I remember correctly this diophantine was solved by Sierpinski in 1956 and there is also a conjecture stating that if $a,b,c$ are phythagorean triples then $a^x+b^y=c^z$ has only the solution $(x,y,z)=(2,2,2)$. But sadly nobody could prove it :...
- Tue May 25, 2021 7:58 am
- Forum: Number Theory
- Topic: Hard Diophantine (maybe)
- Replies: 7
- Views: 11487
Re: Hard Diophantine (maybe)
pythagorean triple? Yeap.(But not so easy to prove).If I remember correctly this diophantine was solved by Sierpinski in 1956 and there is also a conjecture stating that if $a,b,c$ are phythagorean triples then $a^x+b^y=c^z$ has only the solution $(x,y,z)=(2,2,2)$. But sadly nobody could prove it :(
- Mon May 24, 2021 10:52 pm
- Forum: Number Theory
- Topic: Hard Diophantine (maybe)
- Replies: 7
- Views: 11487
Re: Hard Diophantine (maybe)
IDK how it can be done with Fermat's last Theorem , allow me to use Catalan's conjecture instead. Let me state this theorem (it's proven, but the name stayed like this anyway!), Catalan's conjecture : If $x,y,m,n$ are positive integers where $m\geq2, n\geq2$, and they satisfies \[x^m-y^n=1\] then \...
- Mon May 24, 2021 11:46 am
- Forum: Number Theory
- Topic: Hard Diophantine (maybe)
- Replies: 7
- Views: 11487
Hard Diophantine (maybe)
Find all positive integers $x,y,z$ such that $3^x +4^y=5^z$
Disclaimer:
Don't just say done by Fermat's Last theorem
Disclaimer:
Don't just say done by Fermat's Last theorem
- Sun May 23, 2021 9:36 pm
- Forum: College / University Level
- Topic: All About Fractions
- Replies: 5
- Views: 10217
Re: All About Fractions
$1.$ What is the informal (or intuitive) and formal definition of fraction and all kinds of fractions$?$ $2.$ Can we say that $“$a fraction is a number or expression of the form $\dfrac{a}{b}$ or $-\dfrac{a}{b}$ or ${\large c}\dfrac{{\small a}}{\small{b}}$ or $-{\large c}\dfrac{{\small a}}{{\small ...
- Sun May 23, 2021 7:37 pm
- Forum: Social Lounge
- Topic: Struggling with math
- Replies: 6
- Views: 13295
Re: Struggling with math
I suggest that you do Olympiad Math in such a way that will not negatively affect your HSC result. You should focus on HSC. :cry: OK then :( . By the way, how do you guys balance academic and olympiad? Have you guys completed the theory(essential) portion of all 4's and now just practicing? Or, you...
- Sat May 22, 2021 11:09 pm
- Forum: Social Lounge
- Topic: Favorite mathematician?
- Replies: 35
- Views: 80758
Re: Favorite mathematician?
Recent loss for mathematics John Conway.