Thinking in Shapes
Stop seeing just lines and start seeing the hidden patterns that build our world. Learn to measure, build, and solve problems using the logic of shapes.
Like Duolingo, but for Thinking in Shapes. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 26 levels across 3 sections, about 52 minutes end to end, roughly 10 days at five minutes a day. It moves through Build and Measure Your World, Mastering 3D Space, and The Logic Behind the Lines. It starts from scratch.
Free forever · No credit card · iPhone & Android
Key ideas in Thinking in Shapes
- A square frame can hinge at its corners and collapse into a rhombus
- Side lengths lock the angles of a triangle into place
- The concept that side lengths uniquely determine a triangle's shape
- Adding a diagonal creates two triangles, which cannot change shape without changing side lengths
- Unlike a square, a triangle's shape is fixed once the sides are joined
- Why triangles are preferred over quadrilaterals for structural stability
- Knowing all three side lengths (SSS) defines the triangle
- Knowing two sides and the angle between them (SAS) defines the triangle
- Knowing only the angles (AAA) tells you the shape but not the size
- Identifying which sets of information are sufficient to define a specific triangle
- Complex shapes can be broken into simpler rectangles
- Area is a two-dimensional measurement (length times width)
- The total area is the sum of the areas of the smaller parts
- Doubling both dimensions increases area by a factor of four
- Triangles are conceptually half of a related rectangle
- How to calculate the area of an L-shaped floor plan by decomposition
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Thinking in Shapes the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
If you build a triangle using three steel beams of fixed lengths, what happens to the angles between them?
Get it right to open this lesson and 25 more in the app.
How to learn Thinking in Shapes, step by step
Go in order. 26 short levels across 3 sections, about 52 minutes in all, five minutes a day.
- 1
Build and Measure Your World
- The Secret Power of Triangles
- How to Measure Any Flat Space
- Fitting Shapes Together Without Gaps
- Sizing Up Circles and Curves
- 2
Mastering 3D Space
- Turning Flat Drawings Into Solid Objects
- How Much Can This Box Hold?
- The Math of Perfect Pyramids
- Why Spheres Are Everywhere in Nature
- Shadows and Perspective
- Designing Your Own Dream Room
- 3
The Logic Behind the Lines
- Winning Arguments with Geometric Proofs
- Angles: The Language of Turning
- The Rules That Never Change
3 sections · 13 units · 26 levels. Built to play, not to enroll.
Questions about Thinking in Shapes
How do I learn Thinking in Shapes?
Go in order: start with Build and Measure Your World, then Mastering 3D Space, then The Logic Behind the Lines. On Tomo that's 26 short levels, about 52 minutes in all, played five minutes a day. Start free and play the first level in under a minute.
Is there a Duolingo-style app for Thinking in Shapes?
Yes. Tomo works like Duolingo: short daily lessons, streaks and quick quizzes. Thinking in Shapes is one of its free courses, and you can type any other topic to get a course of your own.
Is the Thinking in Shapes course free?
Yes. Thinking in Shapes is playable on Tomo's free plan, which doesn't expire. No credit card, no waitlist. Download the app and start your first lesson.
How long does it take to learn Thinking in Shapes?
26 levels across 3 sections, about 52 minutes of play in total. It's built for five minutes a day, so you finish it a little at a time instead of all at once.
Do I need any background to start Thinking in Shapes?
No. It's pitched at a beginner level, so it starts where you are and builds up. If you can tap a phone, you can start.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Thinking in Shapes is taught in the Bestie style: your friend who just gets it. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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Start Thinking in Shapes today.
Download Tomo, search Thinking in Shapes, and play your first lesson in under a minute.