On Cantor Set Unions
An investigation in fractal geometry and overlapping Cantor-type sets.
Pranav Krishnapuram
Hi, I’m Pranav.
I’m a high school student who spends a lot of time on mathematics. I also like manga and anime, writing, origami, Japanese, and strategy games. This is a place for some of the things I’ve been making, learning, and thinking about.
Some things I like
Math
Proofs, patterns, and problems that are interesting enough to stay with for a long time.
OrigamiTessellations, tiny folds, backlighting, and seeing what a single sheet of paper can do.
Manga & storiesReading them, noticing how they work, and occasionally trying to make my own.
JapaneseI started learning on my own and kept going because the language itself became interesting.
Strategy gamesGo, SET, Hex, Nim — especially games with simple rules and much less simple consequences.
Math, AI, and research
Math is probably what I spend the most time thinking about. I especially like proofs and open-ended problems where it isn’t obvious at the beginning what kind of idea will work. Some of the work below is research; some of it is expository writing, and some comes from exploring how computational tools can be used to solve practical problems.
Constructible Numbers
Research at AIMS Summer School on constructible numbers with Dr. Jonathan Hanke and counselor Eli DeWitt.
Redundancy Degree & Reconstructibility in k-Exact-Perfect Numbers
Number-theoretic research on redundant divisor sets and reconstructibility.
On the Central Limit Theorem and Its Extensions
An expository paper using moment generating functions to develop proofs of forms of the Central Limit Theorem.
An Exposition on Minimal Surfaces
Differential geometry through curvature, catenoids, helicoids, and classical minimal surfaces.
Volume of a Regular d-Dimensional Tetrahedron
A derivation of a closed form for the volume of a regular d-simplex.
Human Detection for Safety Applications Using Deep Learning
Used YOLOv8 transfer learning to detect humans in CCTV footage for workplace safety, achieving 88.5% mAP50 and deploying a virtual barricade alert system. Co-authored with Atul Dubey at AIClub, Mountain View.
Coursework & selected honors
Coursework
Stanford ULO: Linear Algebra; Discrete Mathematics
Euler Circle: Transition to Proofs, Real Analysis, Differential Geometry, Abstract Algebra, Algebraic Topology, Generating Functions
AP exams: Calculus BC (5); Statistics (5)
Selected honors
1st Place, California Science & Engineering Fair — Junior Division, Mathematical Sciences, 2026
Castro Family Award, Synopsys Science Fair — 2026
AIME — 2026; AMC 8 perfect score — 2026
Origami
I’ve been folding for years. Sometimes I’m interested in the geometry of a pattern; sometimes I just like the paper, the repetition, and how different a fold looks when you hold it up to the light.
See the origami gallery →
Manga, anime & things I write
I read a lot of manga and watch anime. I like the way visual stories can do things prose can’t — pacing a joke with a panel break, letting an expression do the work of a paragraph, or leaving something deliberately unsaid. Every so often I try making something myself.
“Soytire”
A short manga about tariffs, trade wars, and a father-son trip to a café. It started as a joke about soybeans and turned into a tiny story about how something happening at the scale of countries can show up in ordinary life.
Read this and other writing →Japanese 日本語
I started learning Japanese on my own because I wanted to understand more of what I was reading and watching without everything passing through translation. Somewhere along the way, learning the language became interesting in its own right.
I like noticing how the same thought changes with formality, word choice, or context, and how much meaning can sit in something that does not translate neatly into English. I’m also interested in the everyday culture around the language — humor, manners, food, history, and the small assumptions stories expect the reader to understand.
Strategy games
I like games where the rules fit on a small piece of paper but the game itself doesn’t. Go is the one I spend the most time on, but I also enjoy SET, Hex, Nim, and other games that turn pattern recognition or a tiny rule set into a lot of strategy.
Go
Territory, influence, shape, and the strange fact that one quiet move can matter much later.
Online-Go Server ↗SET
A fast visual pattern hunt. I like the moment when a set suddenly becomes impossible not to see.
Daily SET puzzle ↗Hex
Simple objective, no draws, and a board that makes connection itself the central problem.
Play Hex ↗Nim
One of those games that looks almost trivial until you discover the mathematics hiding underneath.
Nim puzzle ↗Other things
I also spend time programming, doing debate, and building things with robotics. I like conversations where people disagree thoughtfully, projects where everyone brings something different, and problems where making a quick prototype teaches more than planning for too long.
programming
robotics
debate
anime
visual storytelling
puzzles
Contact
If you want to ask about something here, you can send me a message.