Logarithmic spiral

High school (ages 12+)
Mathematics & Numbers

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/logarithmic-spiral

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the discoverer of the term 'spira mirabilis'?Jacob Bernoulli (late 17th century)
2. What is the key mathematical property?Self-similarity and constant angle between tangent and radial line (equiangular)
3. How does a logarithmic spiral grow differently from an Archimedean spiral?It grows by increasing the distance between turns in a geometric way, so each loop is bigger than the last. The Archimedean spiral keeps the same distance between loops.
4. Why do shells and sunflower seeds have a logarithmic spiral shape?The shape lets new parts grow while keeping the same proportions, so shells, horns, and sunflower seeds stay the same shape as they get bigger.

Self-similarity: A property where a shape exhibits identical patterns at different scales, resembling a fractal.
Geometric Progression: A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Equiangular Spiral: An alternative name for the logarithmic spiral, highlighting its constant angle property.
Phyllotaxis: The arrangement of leaves, branches, flowers, or seeds on a plant stem, often following spiral patterns.