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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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An inequality
JK1603JK   4
N 7 minutes ago by Quantum-Phantom
Source: unknown
Let a,b,c>=0: ab+bc+ca=3 then maximize P=\frac{a^2b+b^2c+c^2a+9}{a+b+c}+\frac{abc}{2}.
4 replies
1 viewing
JK1603JK
Yesterday at 10:28 AM
Quantum-Phantom
7 minutes ago
J
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Inspired by Abelkonkurransen 2025
sqing   1
N 10 minutes ago by kiyoras_2001
Source: Own
Let $ a,b,c $ be real numbers such that $ a^2+4b^2+16c^2= abc. $ Prove that $$\frac{1}{a}+\frac{1}{2b}+\frac{1}{4c}\geq -\frac{1}{16}$$Let $ a,b,c $ be real numbers such that $ 4a^2+9b^2+16c^2= abc. $ Prove that $$ \frac{1}{2a}+\frac{1}{3b}+\frac{1}{4c}\geq -\frac{1}{48}$$
1 reply
1 viewing
sqing
Yesterday at 1:06 PM
kiyoras_2001
10 minutes ago
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Turkey EGMO TST 2017 P6
nimueh   3
N 23 minutes ago by Nobitasolvesproblems1979
Source: Turkey EGMO TST 2017 P6
Find all pairs of prime numbers $(p,q)$, such that $\frac{(2p^2-1)^q+1}{p+q}$ and $\frac{(2q^2-1)^p+1}{p+q}$ are both integers.
3 replies
nimueh
Jun 1, 2017
Nobitasolvesproblems1979
23 minutes ago
J
H
Inspired by Titu Andreescu
sqing   0
26 minutes ago
Source: Own
Let $ a,b,c>0 $ and $ a+b+c\geq 3abc . $ Prove that
$$a^2+b^2+c^2+1\geq \frac{4}{3}(ab+bc+ca) $$
0 replies
sqing
26 minutes ago
0 replies
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No more topics!
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Flag poles
chess64   7
N Wednesday at 10:27 PM by ohiorizzler1434
Source: Canada 1971, Problem 9
Two flag poles of height $h$ and $k$ are situated $2a$ units apart on a level surface. Find the set of all points on the surface which are so situated that the angles of elevation of the tops of the poles are equal.
7 replies
chess64
Jun 24, 2006
ohiorizzler1434
Wednesday at 10:27 PM
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Flag poles
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Reveal topic tags
trigonometry
quadratics
geometry
similar triangles
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Source: Canada 1971, Problem 9
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chess64
4794 posts
chess64
#1 h  Jun 24, 2006, 10:18 PM • 1 Y
Y by Adventure10
Two flag poles of height $h$ and $k$ are situated $2a$ units apart on a level surface. Find the set of all points on the surface which are so situated that the angles of elevation of the tops of the poles are equal.
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Poincare
1341 posts
Poincare
#2 h  Feb 13, 2010, 6:28 PM • 1 Y
Y by Adventure10
Takers? I smell trig!


A very small start
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Poincare
1341 posts
Poincare
#3 h  Feb 13, 2010, 9:54 PM • 2 Y
Y by Adventure10, Mango247
No one? Message is too small. Please make the message longer before submitting.
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gokussj3
223 posts
gokussj3
#4 h  Feb 16, 2010, 9:01 AM • 2 Y
Y by Adventure10, Mango247
I get the answer to be:

$ a\pm\sqrt{a^2-hk}$

@ poincare : Your first equation can be reduced to a quadratic, then solved. :)
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thepisong
23 posts
thepisong
#5 h  Jan 19, 2012, 8:40 PM • 2 Y
Y by Adventure10, Mango247
Don't you get $x=\frac{2ah}{h+k}$ if you solve for the first equation (cross multiplying)
And also, I think it's asking for all the points on the surface, not just between them
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akim99
27 posts
akim99
#6 h  Feb 20, 2016, 11:41 PM • 2 Y
Y by Adventure10, Mango247
The problem becomes significantly easier when we realize that the triangles formed are similar triangles, so instead of trig, just use ratios. ;)
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Durtles
1 post
Durtles
#7 h  Wednesday at 10:19 PM
Y by
I wonder if by "surface" the question means the 2 dimensional surface, ie. you don't have to stand in line with the two flag poles. I got a circle in that case.
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ohiorizzler1434
718 posts
ohiorizzler1434
#8 h  Wednesday at 10:27 PM
Y by
Bruh! There are two possible answers! The obvious one is where the line through the tops of the flag poles meets the ground! The other one is if you imagine one flag pole actually points underground!

Bruh! Let's appreciate the similarity between this and skibidi-insimilicenters! Amazing, right?
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