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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
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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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[*]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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A problem involving modulus from JEE coaching
AshAuktober   2
N 8 minutes ago by clarkculus
Solve over $\mathbb{R}$:
$$|x-1|+|x-2| = 3x.$$
(There are two ways to do this, one being bashing out cases. Try to find the other.)
2 replies
AshAuktober
6 hours ago
clarkculus
8 minutes ago
J
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geometry problem
kjhgyuio   1
N 27 minutes ago by vanstraelen
.........
1 reply
kjhgyuio
Today at 8:27 AM
vanstraelen
27 minutes ago
J
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Inequalities
sqing   4
N an hour ago by sqing
Let $x,y\ge 0$ such that $ 13(x^3+y^3) \leq 125(1+xy)$. Prove that
$$ k(x+y)-xy\leq 5(2k-5)$$Where $k\geq 5.6797. $
$$ 6(x+y)-xy\leq 35$$
4 replies
sqing
Yesterday at 1:04 PM
sqing
an hour ago
J
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Inscribed Semi-Circle!!!
ehz2701   2
N 4 hours ago by mathafou
A right triangle $ABC$ with legs $AB = a$ and $BC = b$ is drawn with a semicircle inscribed into the triangle. What is the smallest possible radius of the semi-circle and the largest possible radius?

2 replies
ehz2701
Sep 11, 2022
mathafou
4 hours ago
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No more topics!
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paper constructions, equilateral + rectangle (May Olympiad 2005 L1)
parmenides51   1
N May 11, 2019 by twinbrian
There are two paper figures: an equilateral triangle and a rectangle. The height of rectangle is equal to the height of the triangle and the base of the rectangle is equal to the base of the triangle. Divide the triangle into three parts and the rectangle into two, using straight cuts, so that with the five pieces can be assembled, without gaps or overlays, a equilateral triangle. To assemble the figure, each part can be rotated and / or turned around.
1 reply
parmenides51
May 11, 2019
twinbrian
May 11, 2019
J
paper constructions, equilateral + rectangle (May Olympiad 2005 L1)
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Reveal topic tags
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parmenides51
30630 posts
parmenides51
#1 h  May 11, 2019, 3:37 AM • 2 Y
Y by Adventure10, Mango247
There are two paper figures: an equilateral triangle and a rectangle. The height of rectangle is equal to the height of the triangle and the base of the rectangle is equal to the base of the triangle. Divide the triangle into three parts and the rectangle into two, using straight cuts, so that with the five pieces can be assembled, without gaps or overlays, a equilateral triangle. To assemble the figure, each part can be rotated and / or turned around.
This post has been edited 1 time. Last edited by parmenides51, Sep 22, 2022, 3:35 PM
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twinbrian
6632 posts
twinbrian
#2 h  May 11, 2019, 5:07 AM • 1 Y
Y by Adventure10
Wait just take the top vertice of the equilateral triangle and trisect it such that it splits the opposite base into $3$ equal parts.
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