This paper was accepted for publishing by NCERT and translated and published in the Gujerati maths E-magazine Suganitam for students.

This research paper explores Aryabhata's groundbreaking contributions to trigonometry. It decodes a 5th-century Sanskrit verse from "Aryabhatiya" to create a 4-decimal-place sine table. The study highlights Aryabhata's unique role as a trailblazer in trigonometry. Accepted for publication in the March 2024 issue of "At Right Angles," the research focuses on teaching forgotten methods to high school students, showcasing India's mathematical tradition from the Vedic era to Madhava's Calculus (circa 1000 BCE to 1600 CE).

The paper expands its scope by emphasizing the continuity in Indian mathematical traditions. It traces the lineage from the Sulbastura's geometric thinking in the Vedic era (circa 1000 BCE) to the advanced Calculus developed by Madhava and his disciples (1350 – 1600 CE). By highlighting this historical continuity, the paper aims to underscore the rich and evolving nature of mathematical thought in India over the centuries.

This paper was accepted for publishing in the Right Angles Mathematics Journal, and the research was presented at the Somaiya College and the St Xaviers College.

This research paper focuses on adapting the Bakhshali algorithm, a fifth-century Indian method for calculating square roots, to address both numerical and algebraic expressions. The algorithm is crucial for initiating a recursion formula for the difference of cosines, aligning it with the modern Taylor Expansion.

The study addresses a historical gap in trigonometric function development, specifically in the construction of cosine tables. While the sine table in Aryabhatiya (499 CE) is well-documented, there is no discussion of the corresponding cosine table for a significant period thereafter. By modifying the Bakhshali algorithm, originally designed for square roots of numbers, the paper extends its application to handle square roots of algebraic expressions. This adaptation allows for the initiation of the recursion formula for the difference of cosines.

The paper also explores the expansions used by the recursion formula, comparing them with the Taylor expansion. With a pedagogical approach, the research aims to highlight the significance of the Bakhshali algorithm in advancing Indian mathematical traditions beyond its historical context, encouraging further exploration and understanding.

This research paper, accepted for publication by Physics Education (Article Reference: PED-103924.R1), investigates the interplay between the center of mass of excised polygons and the presence of the renowned golden ratio. The study explores the problem of determining the center of mass for excised polygons in both two and three dimensions, revealing intriguing connections and occurrences.

The research begins by examining rectangles and rhombi with sides in the ratio of the golden ratio, highlighting certain excised polygons with their center of mass on the edge. This analysis is extended to 3D shapes such as cuboids, pyramids, and cylinders, uncovering three ways of excision that result in balanced objects on the edge.

As the exploration delves into the physics related to the center of mass, the paper uncovers a captivating mathematical coincidence between the golden ratio and the Fibonacci series. Additionally, the research demonstrates and verifies the center of mass location on the edges through 3D-printed objects, providing practical validation to the theoretical findings.