給定任一三角形，求所有平分此三角形面積的線段當中長度最短的一條。

In this report, we attempted to prove Marion’s Theorem with a deductive approach. We also expanded on her discoveries by constructing variations of the original diagram, and attempted to prove the observations and special properties found. The idea was extended to equilateral and isosceles triangles, and then to parallelograms, rhombuses, squares and rectangles. This project has connected the younger generation of mathematicians to the older generations. Although this all started by simply connecting lines together, we have achieved our goal at the end: “Celebrating Marion’s Theorem: Correlation, Construction and Connection”.

During the pandemic of COVID-19, the demand for virus testing dramatically increased, and so did the cost and waste caused by the tests. Traditionally, the subjects are tested individually, meaning that the number of tests conducted is the same as the number of people to receive testing. When a massive population needs to be tested, overloading in laboratories will be led and a tremendous amount of waste will be generated. In this paper, we investigated how to increase the efficiency of conducting tests. We estimate the total amount of tests used by different methods like pooling samples together and doing multiple groupings. We compared the results and found that the multiple grouping model is the optimum solution for our problem.

In this report, we attempted to prove Marion’s Theorem with a deductive approach. We also expanded on her discoveries by constructing variations of the original diagram, and attempted to prove the observations and special properties found. The idea was extended to equilateral and isosceles triangles, and then to parallelograms, rhombuses, squares and rectangles. This project has connected the younger generation of mathematicians to the older generations. Although this all started by simply connecting lines together, we have achieved our goal at the end: “Celebrating Marion’s Theorem: Correlation, Construction and Connection”.

Due to the Covid-19 pandemic outbreak, the use of food delivery services is growing increasingly prevalent in our society. Different food delivery companies have adopted different methods to design routes for delivering orders. Selecting the right route is essential as it directly influences a company’s cost and profit. In order to design the optimal route, one must take into account many factors such as distance, the sequence of orders, the number of orders and customer experience, etc. In our project, we are going to develop a mathematical model to determine the optimal route for one or more riders to deliver food orders.

In this project, we find the probability of winning the coin throwing game. That is, the probability of a coin fitting on tessellated patterns. The tessellation patterns include square, rectangle, equilateral triangle, arbitrary triangle and regular hexagon. General formulas are found depending on the number of tessellated shapes and their size.

We usually play rock, paper or scissors in our daily life to randomly and fairly to determine who is the winner. However, it is quite time-consuming if the number of players increases. We investigate some more ways to play a similar game to Rock Paper Scissors which is more efficient to determine a winner in this project.

During the pandemic of COVID-19, the demand for virus testing dramatically increased, and so did the cost and waste caused by the tests. Traditionally, the subjects are tested individually, meaning that the number of tests conducted is the same as the number of people to receive testing. When a massive population needs to be tested, overloading in laboratories will be led and a tremendous amount of waste will be generated. In this paper, we investigated how to increase the efficiency of conducting tests. We estimate the total amount of tests used by different methods like pooling samples together and doing multiple groupings. We compared the results and found that the multiple grouping model is the optimum solution for our problem.

在這次專題研習中, 我們會從摺紙鶴中分析出當中的數學原理,以及利用我們分析出來的公式，去尋找社會上不同紙鶴作品的原本面積。希望透過這個專題研習向大家展示出摺紙和數學的有趣和奧妙之處，一起從中找到樂趣。

In this project, we aim to plan the evacuation routes of our school as we would like to see if the existing routes can be further improved. We started by taking measurements in the school. Next, we gathered the measurements and created 2 spreadsheets. In sheet 1, we included all venues, staircases and corridors to indicate the travelling time and the number of people that can evacuate along neighbouring venues in all possible routes. Sheet 2 is the planning for all routes and the calculation of the time needed for each route. At last, we will compare the planned routes of this project to the existing evacuation routes.

In this project, we aim to plan the evacuation routes of our school as we would like to see if the existing routes can be further improved. We started by taking measurements in the school. Next, we gathered the measurements and created 2 spreadsheets. In sheet 1, we included all venues, staircases and corridors to indicate the travelling time and the number of people that can evacuate along neighbouring venues in all possible routes. Sheet 2 is the planning for all routes and the calculation of the time needed for each route. At last, we will compare the planned routes of this project to the existing evacuation routes.