Daily Archives: November 6, 2020

2020-20 Efficient triangulation of surfaces

Let \(S_g\) denote the closed orientable connected surface of genus \(g\). Suppose we glue triangles along the edges so that the resulting space is \(S_g\) and the intersection of any two triangles are either empty or a single edge. Let \( n(g) \) be the minimum number of triangles one needs to make \(S_g\) while satisfying the above rule. What are \( n(1), n(2), n(3) \)? Does the limit \( \lim_{g \to \infty} n(g)/g \) exist?

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Solution: 2020-19 Continuous functions

Let \( n \) be a positive integer. Determine all continuous functions \(f: [0, 1] \to \mathbb{R}\) such that
f(x_1) + \dots + f(x_n) =1
for all \( x_1, \dots, x_n \in [0, 1] \) satisfying \( x_1 + \dots + x_n = 1\).

The best solution was submitted by 김유일 (2020학번) Congratulations!

Here is his solution of problem 2020-19.

Other solutions was submitted by 길현준 (수리과학과 2018학번, +3), 채지석 (수리과학과 2016학번, +3), 이준호 (수리과학과 2016학번, +2).

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