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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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idk12345678 Math Contest
idk12345678   21
N a few seconds ago by idk12345678
Welcome to the 1st idk12345678 Math Contest.
You have 4 hours. You do not have to prove your answers.
Post \signup username to sign up. Post your answers in a hide tag and I will tell you your score.*


The contest is attached to the post

Clarifications

*I mightve done them wrong feel free to ask about an answer
21 replies
idk12345678
Apr 10, 2025
idk12345678
a few seconds ago
J
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purple comet math competition question
AVY2024   4
N 24 minutes ago by K1mchi_
Given that (1 + tan 1)(1 + tan 2). . .(1 + tan 45) = 2n, find n
4 replies
AVY2024
2 hours ago
K1mchi_
24 minutes ago
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Inequalities
sqing   25
N an hour ago by sqing
Let $ a,b,c,d>0 $ and $(a+c)(b+d)=ac+\frac{3}{2}bd.$ Prove that
$$\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\geq \frac{20-\sqrt{10}}{3}$$Let $ a,b,c,d>0 $ and $(a+c)(b+d)=ac+\frac{4}{3}bd.$ Prove that
$$\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\geq \frac{21-\sqrt{6}}{3}$$
25 replies
sqing
Dec 3, 2024
sqing
an hour ago
J
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Polynomials
CuriousBabu   3
N 2 hours ago by osszhangbanvan
\[ \frac{(x+y+z)^5 - x^5 - y^5 - z^5}{(x+y)(y+z)(z+x)} = 0 \]
Find the number of real solutions.
3 replies
CuriousBabu
Yesterday at 4:09 PM
osszhangbanvan
2 hours ago
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4 equal reactangle areas in a square (Formula of Unity 2013 gr7)
parmenides51   1
N May 12, 2020 by vanstraelen
A square is divided into five rectangles (see the picture). Prove that if the areas of the four "corner" rectangles are equal then the "central" one is a square.
IMAGE
1 reply
parmenides51
Apr 26, 2020
vanstraelen
May 12, 2020
J
4 equal reactangle areas in a square (Formula of Unity 2013 gr7)
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Reveal topic tags
geometry
rectangle
areas
square
Formula of Unity
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parmenides51
30630 posts
parmenides51
#1 h  Apr 26, 2020, 8:22 AM
Y by
A square is divided into five rectangles (see the picture). Prove that if the areas of the four "corner" rectangles are equal then the "central" one is a square.
//cdn.artofproblemsolving.com/images/5/e/b/5eb37d614c9446b2d1eaddc624a8d7f55bca0609.png
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vanstraelen
8962 posts
vanstraelen
#2 h  May 12, 2020, 8:29 PM
Y by
Area rectangle below $=b \cdot c$, side of the square $=a$.
Area rectangle right $=(a-c) \cdot b$.
Area rectangle above $=(a-d) \cdot e$.
Area rectangle left $=(a-e)(a-b)$.
Eliminating $e$ and $d$ gives $a=b+c$ and $c=d=e$, then the central rectangle is a square.
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