The project aims to find the radius of the inscribed circle of a triangle formed by any 3 given vertices in a regular n-sided polygon with side length 1.

Beyond the traditional constraints of Pick’s Theorem, allowing a rubber band to twist and intersect itself on a geoboard forms triangles with areas smaller than 1/2 square units. In this project, we are investigating the minimal enclosed areas by three straight lines on an “n×n” geoboard for various values of n.

Please refer to the Chinese webpage.

Please refer to the Chinese webpage.

To solve the HKMO problem by alternative solutions, then proof conjectures and propositions generalized from original HKMO problem.

In this project, we designed a defensive city to protect against a giant who wants to reach the center and occupy the city. Our city uses a series of walls in two different shapes: circles (annular) and triangles (trigonal).

This project uses Monte Carlo simulations in Python to evaluate Uno strategies. Comparing defensive card-hoarding with aggressive play, results show the aggressive strategy achieves higher win rates and average scores. Through Expected Risk and Payoff Matrix analysis, the study demonstrates mathematically that continuous attacking is the most effective strategy for winning Uno.

This project evaluates optimal classroom layouts for 34 students, comparing traditional grid, butterfly, and horseshoe layout. By developing a mathematical model to score layouts based on flexibility, visibility, and safety, we aim to determine the arrangement of seats which is mathematically optimal for students.

Please refer to the Chinese webpage.

Please refer to the Chinese webpage.