The Marvelous Mathematics of Sunflowers
What do sunflowers and pinecones have in common with rabbits? What do they all have to do with math? Watch this video from Scientific American’s Instant Egghead series and discover the answer!
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The calculations shown in the video rely on several assumptions. Which of the following assumptions are required to carry out the calculations? Select all the correct answers:
Rabbits start breeding at the age of two months.
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There is no rabbit mortality.
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Adult rabbits need more food than the younger rabbits.
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The rate of reproduction for each pair of rabbits is constant.
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Is the number of clockwise spirals always greater than the number of counterclockwise spirals? It’s hard to tell from the video so check it out for yourself!
What does the expression $360^{0}-\frac{360^{0}}{\phi}$ represent?Select the correct answer:
The golden angle is the complementary angle of another angle.
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The sector of a circle that subtends the golden angle.
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The length of the arc of the circle that subtends the golden angle.
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The supplemental central angle of the golden angle.
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In addition to greater efficiency, the golden angle creates an inflorescence with a more uniform floret spread than any other angle. Other angles create a pattern where most of the inflorescence area is empty. This is demonstrated in computer simulations, here: https://bit.ly/2Y0ecyQ.
How do plants “know” how to arrange their buds in the golden angle? Select the correct answer:
They have a pheromone-based chemical mechanism.
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They have a physical mechanism based on magnetic repulsion.
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They have a growth hormone-based biological mechanism.
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They did all their geometry homework.
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The Marvelous Mathematics of Sunflowers – An interactive video
Play VideoActivity Overview
This video presents the “rabbit problem,” which led to the development of the Fibonacci sequence and the golden ratio. It also shows the sequence in nature and explains why it appears in sunflowers and pine cones. In the activity, students will try to solve problems related to the Fibonacci sequence. Note that question 3 may not be suitable for junior high school students, as it includes the “central angle of a circle” term.
Sequence, general term, angle
Knowledge building
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