Find the area of a leaf through calculus

A leaf
(Image credit: Kumaravel)

After reading Bruce’s post this morning about finding the area of a leaf, it occurred to me that this could be solved using calculus. The basic project would be for students to collect some leaves, trace them onto graph paper, determine through modeling the equations that correspond to the edges of the leaf, and then use integration to find the area as exactly as they can. Students could then confirm their answer works by splitting the area of the leaf into smaller shapes and estimating the total area without calculus.

As an added bonus, students could all choose the same kind of leaf, pool their results, and use some statistics to determine the total area of the leaves in a park, or on their street.

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3 Comments

  • Hi David – love the way you were able to take our very simple investigation with Year 4 and elevate it to something more sophisticated for older kids. What a great way to demonstrate the way to explore a common concept at multiple levels.

  • That sounds like an interesting idea. Have you actually given them that task? How was their reaction?

  • David Wees wrote:

    I haven’t given them the task yet, but once they know a little bit more about integration, I will. I’ll try and come back here and reflect on how well the task goes.

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