This project was completed through team collaboration and combined webpage development, mathematical analysis, interactive simulation, and presentation design into a single learning experience.
During the development process, the team discussed the core ideas of the Buffon-Laplace Needle Problem, the overall structure of the webpages, and how probability theory could be connected with interactive simulation in a clear and intuitive way.
While each member was responsible for different tasks, all members contributed to improving the overall coherence of the project so that the theoretical explanation, simulation behaviour, and webpage presentation could support one another effectively.
In short, By combining theory and visible computational simulation, the project not only demonstrated the fundamental ideas of computational probability modeling, but also highlighted the importance of teamwork in learning and problem solving.
At the beginning of the project, the team first discussed the project topic, webpage structure, and the overall implementation plan.
After the initial planning stage, the work was divided into several major tasks:
Throughout the development process, team members maintained regular communication, shared progress updates, and reviewed each section together to ensure consistency across the webpages. For example, the probability derivations presented in the theory page needed to correspond to the simulation behaviour shown in the demo page, while the parameter settings and user interaction design also needed to remain intuitive and easy to understand.
Through continuous discussion, testing, and revision, the team gradually improved the readability, interactivity, and overall presentation quality of the project. The collaboration process also strengthened communication, coordination, and teamwork skills among team members.
Responsible for implementing the interactive simulation on the Demo page and designing the overall webpage interface. This included developing the simulation controls, parameter input layout, canvas-based visual display, dynamic statistics updates, and the general visual style of the website. The work also involved making sure that the simulation behaviour, page navigation, and overall user experience were clear, consistent, and suitable for an offline educational presentation.
Responsible for organising the project topic and preparing the presentation materials for the final demonstration. This included researching how to present the project more clearly and effectively, planning the structure of the live demonstration, and coordinating how the webpages, theory, and experimental results should be introduced during the presentation. The work also involved summarising the simulation results and the overall project workflow so that the final presentation could explain both the technical implementation and the learning process in a coherent way.
Responsible for researching and explaining the mathematical theory behind the Buffon-Laplace Needle Problem. This included organising the historical background, probability assumptions, crossing conditions, derivation of the probability formula, and the method used to estimate π through repeated simulations.
I have gained practical experience in applying front-end web development skills (including HTML, CSS, and JavaScript) in real project environments, rather than merely focusing on classroom exercises. I have learned how to use JavaScript Canvas to create interactive visual simulations, as well as to utilise more modern and easily manageable layout organisation methods, embed mathematical formulas and other web practical skills in web pages. Moreover, my understanding of user-friendly interface design has deepened.
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Through working on the projrct, I developed a deeper understanding of geometric probability and how mathematical concepts can be connected with interactive simulation and visualisation. By helping design and test different parts of the project, I learned how computational experiments can be used to approximate theoretical results and make abstract probability concepts easier to understand. I also improved my ability to connect the mathematical explanation with the practical implementation throughout the development process.
The creative aspect of the project is the combination of:
Instead of only presenting formulas, the project allows users to visually observe how repeated random experiments gradually approach the theoretical probability and the value of π.
By combining theoretical explanation with dynamic simulation, the project makes the Buffon-Laplace Needle Problem more intuitive, interactive, and easier to understand.
The project has several strengths:
However, the project still has some limitations. Some mathematical details were simplified to make the explanation easier to understand, and the current simulation mainly focuses on the basic Buffon-Laplace model.
In the future, the project could be improved by adding more statistical analysis, better data visualisation, and additional interactive features to provide a richer learning experience for users.