Geometry Quote by Walter Isaacson
““On what may be the last page he wrote in his notebooks, Leonardo drew four right triangles with bases of differing lengths (fig. 143). Inside of each he fit a rectangle, and then he shaded the remaining areas of the triangle. In the center of the page he made a chart with boxes labeled with the letter of each rectangle, and below it he described what he was trying to accomplish. As he had done obsessively over the years, he was using the visualization of geometry to help him understand the transformation of shapes. Specifically, he was trying to understand the formula for keeping the area of a right triangle the same while varying the lengths of its two legs. He had fussed with this problem, explored by Euclid, repeatedly over the years. It was a puzzle that, by this point in his life, as he turned sixty-seven and his health faded, might seem unnecessary to solve. To anyone other than Leonardo, it may have been.””
About This Quote
Source Book: Leonardo da Vinci, Walter Isaacson, 2017
Leonardo used geometric drawings to explore how to keep a right‑triangle’s area constant while changing its leg lengths, reflecting his lifelong habit of visual problem solving.
In simple terms: He tried to keep triangle area same while legs change.
Key Takeaway
Use visual models to explore complex problems.
Themes
creativity
problem solving
geometry
visualization
Mood
curious
reflective
Type
historical
analytical
When to use this quote
- mathematical research
- engineering design
- educational illustration
- personal reflection
Key Concepts
mathematics
proportional reasoning
invariant properties
Questions to Reflect On
- How can visual thinking aid abstract reasoning?
- When is a visual approach unnecessary?
A Different Perspective
The method may be seen as impractical late in life, and not all problems benefit from visual abstraction.
![“Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we…” quote by Jean le Rond d'Alembert](https://sms4smile.com/quotes/img-quotes/0d9/jean-le-rond-d-alembert-26487_able_geometry-which-should-only-obey-physics_6945.jpg)
