Unraveling profound solutions with mathematical rigor.
Math IA: Optimal Room Orientation to Minimize Solar Incidence
Manu Anish — September 2023
In this paper I develop a mathematical model to calculate the solar incidence on a room. The model is then used to calculate the optimal room orientation for a given location and room size. The paper concludes by discussing the limitations of the model and possible extensions.
ROSS Celebration II : Cyclicity of the Unit Group
Manu Anish, Carol Bao — July 2023
My ROSS Family's (11) presentation slides on the cyclicity of the unit group of a finite field (part of the Ross Mathematics Program).
ROSS Celebration I : Fundamental Theorem of Arithmetic
Manu Anish, Charlie Jiang, BangTam Ngo, Carol Bao — June 2023
My ROSS Family's (11) submission for the ROSS Celebration (part of the Ross Mathematics Program). We prove the Fundamental Theorem of Arithmetic from first principles starting from ring and order axioms.
TOK Exhibition: Are Some Things Unknowable?
Manu Anish — April 2023
My submission for the TOK Exhibition (part of the IB Diploma Programme).
Investigating Bio-mimetic Origami Radiation Shield Design Geometries for Mitigating Transient Soft Errors Induced by Cosmic Rays in Solid-State Storage Devices
Manu Anish, Eliza Kishan, Maria de los Angeles Delgado Alvarez, Nikolai Voth — April 2023
This research investigates the impact of radiation exposure from hadrons of terrestrial cosmic rays (primarily neutron, proton, and pion) on solid-state storage devices, specifically focusing on the transient effects that cause single event upsets (SEUs) or soft errors. The experiment involves measuring soft-error rates of a commercially available solid-state storage device controlled by NodeMCU micro-controller when exposed to hadron beams from the T9 PS accelerator that simulate terrestrial cosmic radiation exposure. In particular, we propose to test the shielding efficacy of different origami geometric radiation shield designs, bio-mimetically inspired by the cellular structure of radiation resistant Melanized fungi. The proposed experiment draws on two strands of previous studies -- radiation induced soft errors in solid state devices, and geometric cellular structure of radiation-resistant fungi in shielding. The results of this study will potentially contribute to the development of new bio-mimetic origami geometric design philosophies and principles for radiation shield designs.
Musical Instrument Design: A Mathematical Approach
Manu Anish — May 2022
An exploration of the intersection of physics and music by designing a unique musical instrument inspired by the guitar. Leveraging principles of wave mechanics and harmonic analysis, I developed a novel computational framework to calculate the precise positions of frets and corresponding notes on the instrument.
A Novel Holomorphic Form of the Collatz Conjecture
Manu Anish — November 2021
This paper describes some functional equations which occur connected with the famous Collatz Conjecture. In particular, it discusses two functional equations of the Collatz Problem. Using the Roots of Unity similar modular functions are generalized into functional equations.
A Proof Without Words: The Harmonic Division Theorem
Manu Anish — May 2021
The Harmonic Division Theorem is a simple yet powerful result in elementary origami. It allows the division of a line segment into any number of equal parts. In this paper, I present a proof of this theorem using only elementary geometry and trigonometry. The proof is a visual one, and is hence a proof without words.