# dyna3

A dynamical geometry exploration tool

Slides © 2025 by Studio Infinity, licensed under CC BY-SA 4.0

### Purpose

#### Tasks

- Explore geometric objects
- Solve geometry problems

#### Representations

- Described in terms of constraints
- Fundamentally three-dimensional

### Status

- We have an engine that works for at least some simple problems
- We have enough of an interface to start testing the engine interactively

## Demos

### How spiky is a tetrahedron?

- Take a regular tetrahedron
- Inscribe a sphere in it
- Circumscribe a sphere around it
- What’s the ratio of the spheres’ radii?

### Irisawa’s hexlet

A temple problem by Irisawa Shintarō Hiroatsu (1822)

From “Sangaku of Soddy's hexlet in Samukawa Shrine” by Shikishima Ken-ichi, licensed under CC BY-SA 3.0

#### Setup

- Six solid spheres form a cyclic chain, each one touching the next
- Two solid spheres, the “sun” and the “moon,” each touch all the chain spheres
- A hollow outer sphere encloses and touches all the other spheres

#### Problem

Fix the diameters of these spheres:

Outer | 30
Sun | 10
Moon | 6
One chain sphere | 5

What are the diameters of the other chain spheres?

## Plans

For summer–fall 2025

### Narrow

- Make the engine more robust
- Expand our corpus of test problems
- To support engine testing, improve the interface as needed

### Broad

- Explore the “island of usefulness” of our current engine approach
- Either find some of its boundaries or show that it covers a large swath of interesting problems