## Add Your Heading Text Here

# BRAINSTORMER - BOOK

# by Janaka Rodrigo

## PREFACE

Most of us are born lateral thinkers, naturally inclined to use nontraditional and unconventional approaches to problem-solving. This type of thinking is crucial for developing creativity and exploratory skills. However, many lose their lateral thinking abilities in schools and universities due to the adoption of vertical thinking, which emphasizes strict adherence to rules and focusing on a single answer. This approach limits our brains to a fixed frame, giving very little opportunity to enhance exploratory skills in mathematics.

In my first prime document “**The Possibilities are Infinite**”, I have provided numerous examples where lateral thinking is essential to transforming the reader into an explorer. Preparing students’ mindsets before they enter secondary education is crucial for them to fully benefit from this document. Therefore, I prepared the second prime document, “**Maths Projects for Grades 8, 9, 10, and Ordinary Level Students**,” which introduces maths activities for students up to the ordinary level standard.

This third document **BRAINSTORMER** consists of a **new concept** of combinatorial geometry, **17 new sequences** in mathematics published on the OEIS, and **7 new proofs**. Among these is a fully trigonometric proof of Pythagoras’ theorem that does not rely on the properties of similar triangles, and the first-ever single proof of both the Sine Law and the Cosine Law. Related articles not only introduce novel approaches but also guide readers in formatting manuscripts to international standards . Additionally, it includes the **Humanistic Mathematics Activity-Based Project**, a pioneering initiative in mathematics education in Sri Lanka. This document aims to provide significant evidence that supports my vision articulated in the first document. The positive feedback from senior lecturers at leading universities, who reviewed the first document, further validates this vision. As a result, users can be confident in the value of the information provided in the first document, which aim to transform the current system of mathematics education into a more contextual teaching and learning process. This transformation holds the promise of producing mathematicians who can appreciate the importance of mathematical issues, view the world through the lens of mathematics, describe both physical activities and the wonders of nature in mathematical terms, tackle global challenges, and create their own challenges and conjectures that extend beyond conventional human understanding . I believe that the provided mathematical models and computer programs will be helpful for the students who are doing ICT as a subject and academics in their research within the software field, ultimately fulfilling the goals of 21st century mathematics education.

I extend my sincere gratitude to the board of editors of the **Online Encyclopedia of Integer Sequences** for recognizing the importance of new concepts and assisting in drafting my submissions to international standards. My heartfelt thanks go to the editors of the **Mathematical Association of America** journals for reviewing my submissions and providing valuable feedback. Special thanks to **Rev. Bro. Director Dr. Pubudu Rajapaksha** for his support in initiating the Humanistic Mathematics Activity-Based Project at the college, and to the **senior university lecturers of mathematics** for their commitment in reviewing my proposals.