Assignments & Lessons

Before watching (3 min) — Teacher writes these questions on the board:

1. Who was Vitruvius? What did he believe about the human body?
2. What is the connection between a circle and a square in Da Vinci's famous drawing?
3. What ancient problem was Leonardo trying to solve?
4. What does the word proportion mean to you?

Watch first 8 minutes. Students take brief notes. Then pair discussion (5 min): circle = divine/infinite; square = stability/order. The drawing bridges both.

Teacher introduces 10 key words. Students copy into notebooks:

Students read the Abstract and Introduction (8 min) silently. Underline vocabulary from Stage 2.

Comprehension check — individual (5 min):

1. What are the three honest goals the paper states?
2. What historical document does the paper reference, and how old is it?
3. What is the "Rhind approximation" of π, and how accurate is it?
4. What does the author mean by calling a conjecture "honestly marked sorry"?
5. In your own words: what is this paper really about?

Teacher reviews whole-class (7 min). Focus on intellectual honesty. Connect to the video: Leonardo also worked at the edge of what was knowable.

1. The fraction 22/7 is a well-known ____________ for the value of π.
2. Mathematicians have proven that π is ____________, meaning no polynomial equation with whole-number coefficients can produce it.
3. A ____________ number can always be written as p divided by q, where both are integers.
4. The continued-fraction expansion of π produces ____________ like 333/106 and 355/113 that get closer and closer to the true value.
5. Vitruvius believed that ____________ in architecture reflected the ____________ of the human body.
6. A ____________ is an idea that seems very likely to be true but has not yet been fully proven.
7. The G-cycle is an ____________ chain that applies a series of transformations to circle data.
8. The research team used Lean 4 to ____________ the theorems and make them verifiable by computer.
9. The GCM ____________ provides a structured set of rules for modelling contact dynamics across many different systems.

Rewrite these sentences in the passive:

Option A — Summary: Summarise the paper in your own words. What problem does it address? What does it find? What does it admit it cannot yet prove? Use at least 6 vocabulary words from today's lesson.

Option B — Personal Response: What idea from today's lesson surprised you, moved you, or made you think differently? Connect it to your own life, background, or learning experience.

Option C — The Dedication: The paper opens: "Neither of them read from a recipe book. Both of them ate the cake. This is what education is, and what it is not." What do you think this means? Do you agree?

Discuss in pairs, then write 3–5 sentences for each:

1. Think of something important you learned by doing rather than by following instructions. What was it? How did it feel to figure it out yourself?
2. π cannot be written exactly. We use approximations (22/7, 355/113) because they are good enough. Can you think of other areas of life where a "good enough" answer is more useful than a perfect one that doesn't exist?
3. This paper connects ancient Egypt, Renaissance Italy, and modern Newark. Where do you come from, and what knowledge did you bring with you?