The High School Gap

See you on the other side.

DISCLAIMER

While I’ve observed this phenomenon independently early on, I cannot take credit for being the first to point it out. I first heard the version I will be elaborating on in Mar del Plata, July 2012. The diagrams, further explanation, and tips below, however, are my original work.

I am not (yet) an expert in mathematics education, and the explanations and diagrams below come from my personal observations and not from any formal study. If you want to subject this phenomenon to research, however, do consider e-mailing me. I’d be happy to help!

Problem Post 2-2: A Sampler of `Olympiad' Geometry Concepts

Problem Posts

[Level 4]
Henry

This post is meant to be a `sampler' of sorts, to show the most common tag words one will see in olympiad geometry problems.

I've been fortunate enough to find two remarkable problems, and solve them in ways that form a whirlwind tour of the subject. The first problem demonstrates side chasing, isosceles triangles, some cyclic quadrilaterals and spiral similarity. The second problem demonstrates power theorems, cyclic quadrilaterals, collinearity, and triangle geometry.

Problem 1

This one comes from Andreescu and Gelca's Mathematical Olympiad Challenges.

QUESTION
(Andreescu, Gelca) Let $B$ and $C$ be the endpoints and $A$ the midpoint of a semicircle. Let $M$ be a point on the line segment $AC$, and $P$, $Q$ the feet of the perpendiculars from $A$ and $C$ to the line $BM$, respectively. Prove that $BP=PQ+QC$.

Mathletes’ Greatest Secrets Finally Revealed Episode 6: Mathematics Olympiad Summer Camp

Mathletes’ Greatest Secrets Finally Revealed

Episode 6: Mathematics Olympiad Summer Camp
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Henry

Screenshot from imo-official.com

If you make it all the way, your name ends up on this site. For better or for worse. Forever.

Each year the Mathematics Olympiad Summer Camp selects and trains the Philippine Team for the International Mathematical Olympiad.

If you’re a high school senior, this will probably the last training-contest circuit you will be doing before entering university. Everybody else in your batch will have hung the gloves before you do. Know that whatever happens, you’ve been given the rare honor of staying in the ‘Math Games’ until the very end.

Mathletes’ Greatest Secrets Finally Revealed Episode 5: Philippine Mathematical Olympiad

Mathletes’ Greatest Secrets Finally Revealed

Episode 5: Philippine Mathematical Olympiad
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Henry

Image Credit: "weird pi sculpture at the lavender farm" by Brian Ellin. Licensed under CC BY-NC-SA 2.0.

The letter pi is a apt motif that recurs in each yearly iteration of the PMO logo.

The Philippine Mathematical Olympiad is the premier mathematics contest for high school students in the country. Among the contests and programs we’ve discussed, only this one bears the legitimacy of being the country’s national Olympiad.

Mathletes’ Greatest Secrets Finally Revealed Episode 4: Mathematics Trainers' Guild

Mathletes’ Greatest Secrets Finally Revealed

Episode 4: Mathematics Trainers' Guild

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Henry

(Image credit: publicdomainpictures.net)

YMIITP often brings participants to interesting locales around the country.

The Mathematics Trainers’ Guild offers one of the largest scale training programs in the country, and sends participants to a large variety of international events. It also keeps quite a high profile – if you perform, you will likely see your name in the papers.