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a My Retirement & New Leadership at AoPS
rrusczyk   1350
N 10 minutes ago by aaaand
I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE
1350 replies
rrusczyk
Monday at 6:37 PM
aaaand
10 minutes ago
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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
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Comparing inradii of triangles
Ankoganit   11
N a minute ago by maths_enthusiast_0001
Source: India TST 2016 Day 4 Problem 1
Let $ABC$ be an acute triangle with circumcircle $\Gamma$. Let $A_1,B_1$ and $C_1$ be respectively the midpoints of the arcs $BAC,CBA$ and $ACB$ of $\Gamma$. Show that the inradius of triangle $A_1B_1C_1$ is not less than the inradius of triangle $ABC$.
11 replies
Ankoganit
Jul 22, 2016
maths_enthusiast_0001
a minute ago
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Inspired by old results
sqing   0
5 minutes ago
Source: Own
Let $a,b,c$ be real numbers.Prove that
$$\frac{ (a-b)(b-c)(c-a)}{ (a^2+1)(b^2+1)(c^2+1)}\leq\frac{3\sqrt 3}{8}$$$$\frac{ (a-b)(b-c)(c-a)}{ (a^2+2)(b^2+1)(c^2+2)}\leq\frac{3}{8}\sqrt{\frac{3}{2}}$$$$\frac{ (a-b)(b-c)(c-a)}{ (a^2+3)(b^2+1)(c^2+3)}\leq\frac{3}{8} $$$$\frac{ (a-b)(b-c)(c-a)}{ (a^2+3)(b^2+2)(c^2+3)}\leq\frac{3}{16} $$
0 replies
sqing
5 minutes ago
0 replies
J
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An easy inequality
jokehim   1
N 5 minutes ago by Nguyenhuyen_AG
Source: my problem
Prove that $$\frac{a}{a^2+bc}+\frac{b}{b^2+ac}+\frac{c}{c^2+ba}\ge \frac{3}{a+b+c},\ \ \forall a,b,c\ge 0: a+b+c>0.$$
1 reply
jokehim
27 minutes ago
Nguyenhuyen_AG
5 minutes ago
J
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Long polynomial factorization
wassupevery1   1
N 12 minutes ago by Photaesthesia
Source: 2025 Vietnam IMO TST - Problem 6
For each prime $p$ of the form $4k+3$ with $k \in \mathbb{Z}^+$, consider the polynomial $$Q(x)=px^{2p} - x^{2p-1} + p^2x^{\frac{3p+1}{2}} - px^{p+1} +2(p^2+1)x^p -px^{p-1}+ p^2 x^{\frac{p-1}{2}} -x + p.$$Determine all ordered pairs of polynomials $f, g$ with integer coefficients such that $Q(x)=f(x)g(x)$.
1 reply
+1 w
wassupevery1
5 hours ago
Photaesthesia
12 minutes ago
J
No more topics!
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J
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Number of sign change in cos ka
Rohit-2006   2
N Mar 23, 2025 by Rohit-2006
Let $0\leq\alpha\leq\pi$. Denote by $V_n(\alpha)$ the number of changes of signs in the
sequence
$$1, cos \alpha, cos 2\alpha, . . . , cos n\alpha.$$Then prove that
$$\lim_{n\rightarrow\infty}\frac{V_n(\alpha)}{n}=\frac{\alpha}{\pi}$$.
2 replies
Rohit-2006
Mar 23, 2025
Rohit-2006
Mar 23, 2025
J
Number of sign change in cos ka
G H J
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algebra
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G H BBookmark kLocked kLocked NReply
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Rohit-2006
167 posts
Rohit-2006
#1 h  Mar 23, 2025, 2:48 PM
Y by
Let $0\leq\alpha\leq\pi$. Denote by $V_n(\alpha)$ the number of changes of signs in the
sequence
$$1, cos \alpha, cos 2\alpha, . . . , cos n\alpha.$$Then prove that
$$\lim_{n\rightarrow\infty}\frac{V_n(\alpha)}{n}=\frac{\alpha}{\pi}$$.
This post has been edited 3 times. Last edited by Rohit-2006, Mar 23, 2025, 3:17 PM
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sanyalarnab
924 posts
sanyalarnab
#2 h  Mar 23, 2025, 3:15 PM
Y by
Ig you missed writing $\lim_{n\to \infty}$ :D
Z K Y
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Rohit-2006
167 posts
Rohit-2006
#3 h  Mar 23, 2025, 3:17 PM
Y by
Oha sorry...mne likhte vule gechi...akta hint dao...piecewise function considered korar por ki korbo?....scaling er change ta kivabe track korbo
This post has been edited 1 time. Last edited by Rohit-2006, Mar 23, 2025, 3:21 PM
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