Why colliding blocks compute pi

Item: Why colliding blocks compute pi
Rating: 5
Author: PostSingularity Institute

by 3Blue1Brown (Grant Sanderson)

Formal & Physical Sciences Science — General & History PDZPopular science PDZMPopular and recreational mathematics

🎙 3Blue1Brown (Grant Sanderson) 👥 8.6M 📅 March 13, 2025 ⏱ 26 min 👁 6.3M 📄 science communication 🧭 2026-08-28

Available in: English (current) Français

Keywords

picolliding blocksconservation lawssmall angle approximationGrover's algorithm

Summary

This video revisits the classic 3Blue1Brown problem where two blocks colliding on a frictionless plane produce the digits of pi. Grant Sanderson recaps the original setup: a small block and a large block collide elastically, with a wall on the left, and the total number of collisions equals the digits of pi when the mass ratio is a power of 100. He then introduces a state-space approach, mapping velocities to a circle via energy conservation, and shows how the problem reduces to a geometric puzzle of counting arcs on a circle. Using the inscribed angle theorem and small angle approximations, he explains why the number of collisions matches pi’s digits. The video also highlights the subtlety that the full connection to pi is technically an unsolved problem, as it depends on a conjecture about the digits of pi. Finally, he teases a connection to quantum computing, specifically Grover’s algorithm, which is explored in a follow-up video. The explanation is clear, rigorous, and visually compelling, making advanced mathematical concepts accessible.

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Critical Evaluation

Value of the Information & Strength of the Argument

The video provides deep insight into a surprising mathematical phenomenon, offering a rigorous derivation from conservation laws to a geometric interpretation. The argumentation is solid, building step-by-step from physics to geometry to number theory. The use of state space and the inscribed angle theorem is elegant and well-motivated. The discussion of the unsolved conjecture adds intellectual honesty and depth, showing the limits of current mathematical knowledge. The connection to quantum computing is intriguing and well-referenced, though only briefly touched upon in this video.

Scientific Rigor, Source Quality, Title Accuracy

The video maintains high scientific rigor, with clear derivations and proper acknowledgment of idealizations. It cites the original paper by Gregory Galperin and Adam Brown’s paper on the analogy with Grover’s algorithm, both provided in the description. The title accurately reflects the content. The video is well-structured with timestamps, and the creator’s comments address common misconceptions, further enhancing credibility. The use of small angle approximations is justified with Taylor series, and the unsolved nature of the pi connection is honestly presented.

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Title / Content Match

The title accurately reflects the content, which explains the surprising appearance of pi in a block collision problem.

Quality & Reliability

9/10

High-quality mathematical exposition with rigorous derivations, clear visualizations, and honest discussion of the unsolved conjecture regarding pi's digits. The video builds on a well-known problem and connects it to quantum computing, citing original papers.

Chapters

Cited Sources

Galperin, Playing pool with pi — Original paper on the block collision problem and its connection to pi.
Adam Brown, Quantum search and the block collision problem — Paper on the analogy between the block collision problem and Grover's algorithm.
Interactive simulation of colliding blocks — Interactive tool built by a viewer to explore the problem.
Matt Parker's Pi Day video — Video about attempting to demonstrate the block collision phenomenon in practice.
NY Times blog post about the problem — Blog post discussing the block collision problem and pi.

Concurring Sources

Galperin, Playing pool with pi — Original paper confirming the block collision result.
Adam Brown, Quantum search and the block collision problem — Paper supporting the connection to Grover's algorithm.

External References

Contribution & Novelties

This video provides a fresh perspective on a well-known problem, offering a deeper geometric explanation and highlighting the unsolved conjecture about pi’s digits. It also introduces a connection to quantum computing, specifically Grover’s algorithm, which is a novel and intriguing link. The video’s clear visualizations and step-by-step reasoning make the mathematics accessible while maintaining rigor.

Pour aller plus loin :

Grover’s algorithm — Quantum algorithm for unstructured search, related to the block collision problem.
Inscribed angle theorem — Geometric principle used to show equal arcs on the circle.
Small-angle approximation — Approximation used to relate the angle to the mass ratio.
Pi — Mathematical constant central to the video’s theme.

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Radar Profile

The radar profile shows high scores across all dimensions, with particularly strong quality of information and technical level. The video excels in providing rigorous, well-explained content with a high degree of reliability, making it an excellent educational resource.

Reliability 9/10

💬 Très positif. Sur les 30 commentaires analysés, le public exprime une admiration et une gratitude massives pour la clarté et la profondeur de l'explication, avec de nombreux témoignages personnels sur l'impact éducatif de la chaîne.