# The 3-4-7 miracle. Why is this one not super famous? | Summary and Q&A

569.2K views
December 30, 2021
by
Mathologer
The 3-4-7 miracle. Why is this one not super famous?

## TL;DR

Points perform dances in various geometric patterns, which can be explained using the principles of circle rolling and the coin rotation paradox.

## Key Insights

• ⭕ Points moving along straight lines and circles simultaneously can be explained using the concept of circle rolling.
• 🤣 Spirographs, generated by rolling circles, can create a variety of mathematical curves and geometric patterns.
• 🪙 The coin rotation paradox helps explain the counterintuitive number of rotations observed when one coin rolls around another.

## Transcript

welcome to another mathologer video recently while browsing maths on the web and working on a hardcore video i got sidetracked by a very puzzling animation have a look there are 12 points performing a strange dance in certain groups of three the points are waltzing in equilateral triangles at the same time in certain groups of four they're performi... Read More

## Questions & Answers

### Q: How are the points in the animation able to move in both straight lines and circles simultaneously?

This phenomenon can be explained by the concept of circle rolling, where a smaller circle rolls inside a larger one, causing points on its perimeter to trace out various shapes.

### Q: What are hypertrochoids, and how are they related to the animation?

Hypertrochoids are curves formed by tracing a point on a rolling circle as it moves inside a larger circle. In the animation, the points create the shapes of equilateral triangles and other geometric figures.

### Q: Why does the animation feature a star made up of straight line segments instead of curved lines?

The animation cheats a bit by replacing a curved star with a star consisting of straight lines. This simplification allows for easier visualization of the dancing points' movements.

### Q: How does the coin rotation paradox explain the number of rotations observed in the animation?

The coin rotation paradox demonstrates that when a smaller coin rolls around a larger one, the number of rotations is determined by the ratio of their circumferences. This principle can be applied to understand the number of rotations in the animation.

## Summary & Key Takeaways

• The video explores a puzzling animation of points dancing in different geometric patterns, including equilateral triangles and squares.

• The phenomena observed in the animation can be understood by applying the principles of circle rolling and the coin rotation paradox.

• Spirographs, mathematical curves generated by rolling circles, are used to create the patterns observed in the animation.