Why is there less geometry problems lately?

Why is there less geometry problems in the Geometry and Combinatorics section lately?

Note by Zi Song Yeoh
4 years, 10 months ago

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Yup, only two n this week's set.

Akshat Jain - 4 years, 10 months ago

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There are much fewer geometry problems that we can ask at the higher levels. Most of our geometry problems are capped below 200 points, and even then they have a disproportionate percentage of correct answers with little understanding. Level 5's will see 2-3 geometry problems a week, while level 4's will see 3-4 geometry problems. To a slight extent, something similar happens with Algebra and Number Theory, though the distinction is less stark.

For more context, you can read the discussion Combinatorics and Geometry, which provides more details. Some of the relevant excerpts are:

Sad to say, pure Euclidean geometry does not have much applications. There are almost no further theory that I could allude to, as opposed to concepts in Algebra, Number Theory and Combinatorics. The 'university equivalent' is Topology, but this does not go well with the high school students, who do not see the relevance to Euclidean geometry (because there is little).

The math olympiad world does love geometry problems, in part because geometry proofs require very rigorous demonstrations with little ambiguity (e.g. at IMO they deduct 1 point if you do not explain why a defined point is inside or outside of a triangle). However, in fitting with our numerical answer system, it becomes next to impossible to require exact proofs of such statements.

As you pointed out in another post, there are questions which could be approached by making various assumptions which are not indicated in the question, in order to get the 'short-cut' to the answer. Furthermore, accurate diagrams could be drawn, in order to get estimates of lengths and angles in the problem, without requiring much work. This is obvious in solutions where students say "Since θ=31.4159∘, hence cosθ=…".As such, these problems are much less a reflection of your problem solving ability, as opposed to your "crunching" ability.

Calvin Lin Staff - 4 years, 10 months ago

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