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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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 upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
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Inequalities
sqing   9
N 11 minutes ago by sqing
Let $ a,b> 0 , \frac{a}{b^2}+\frac{b}{a^2}+\frac{56}{(a+b)^2} \leq 16.$ Prove that
$$ab(a+b) \geq 2$$Let $ a,b> 0 ,\frac{1}{a^2}+\frac{1}{b^2}+\frac{28}{(a+b)^2} \leq 9.$ Prove that
$$ab(a+b) \geq 2$$
9 replies
1 viewing
sqing
May 25, 2025
sqing
11 minutes ago
J
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rare creative geo problem spotted in the wild
abbominable_sn0wman   3
N 2 hours ago by jasperE3
The following is the construction of the twindragon fractal.

Let $I_0$ be the solid square region with vertices at
\[ (0, 0), \left(\frac{1}{2}, \frac{1}{2}\right), (1, 0), \left(\frac{1}{2}, -\frac{1}{2}\right). \]
Recursively, the region $I_{n+1}$ consists of two copies of $I_n$: one copy which is rotated $45^\circ$ counterclockwise around the origin and scaled by a factor of $\frac{1}{\sqrt{2}}$, and another copy which is also rotated $45^\circ$ counterclockwise around the origin and scaled by a factor of $\frac{1}{\sqrt{2}}$, and then translated by $\left(\frac{1}{2}, -\frac{1}{2}\right)$.

We have displayed $I_0$ and $I_1$ below.

Let $I_\infty$ be the limiting region of the sequence $I_0, I_1, \dots$.

The area of the smallest convex polygon which encloses $I_\infty$ can be written as $\frac{a}{b}$ for relatively prime positive integers $a$ and $b$. Find $a + b$.
3 replies
abbominable_sn0wman
Yesterday at 6:04 PM
jasperE3
2 hours ago
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Find the number of ordered triples (p,q,r)
Darealzolt   3
N 3 hours ago by ohiorizzler1434
Let \(p,q,r\) be prime numbers such that
\[ \frac{1}{pq}+\frac{1}{qr}+\frac{1}{pr}=\frac{1}{839} \]Hence find the numbers of ordered triples \(\{p,q,r\}\)
3 replies
Darealzolt
Yesterday at 1:52 PM
ohiorizzler1434
3 hours ago
J
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Great Geometry with Squares on sides of triangles
SomeonecoolLovesMaths   4
N 3 hours ago by ohiorizzler1434
Three squares are drawn on the sides of triangle \(ABC\) (i.e., the square on \(AB\) has \(AB\) as one of its sides and lies outside \(ABC\)). Show that the lines drawn from the vertices \(A\), \(B\), and \(C\) to the centers of the opposite squares are concurrent.

IMAGE
4 replies
SomeonecoolLovesMaths
May 22, 2025
ohiorizzler1434
3 hours ago
J
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right triangle construction (2014 From Tasks to Tasks, p15 Ukr)
parmenides51   0
May 3, 2021
Construct a right triangle given the hypotenuse and the median drawn to the leg.
0 replies
parmenides51
May 3, 2021
0 replies
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right triangle construction (2014 From Tasks to Tasks, p15 Ukr)
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parmenides51
#1 h  May 3, 2021, 7:13 AM
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Construct a right triangle given the hypotenuse and the median drawn to the leg.
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