Bamboozled by Prime Numbers

SCIENCE

One species of bamboo flowers every 120 years. Another flowers every 32 years. Another flowers every 60 years. And now, biologists have suggested a tantalizing hypothesis: bamboo cycles have reached their remarkable lengths through some simple arithmetic. (The Loom, Nat Geo)

Understand how math is the language of science with our introductory encyclopedic entry on quantitative data.

Teachers, scroll down for a quick list of key resources in our Teachers’ Toolkit.

Bamboo is the world’s largest species of grass—which I suppose makes this tranquil forest in Nanjing, Jiangsu, China, a beautifully manicured lawn. Bamboo’s sturdy, fibrous texture leads many organizations to consider it a forestry product, however—a tree. Photograph by Luis Marden, National Geographic

Bamboo is the world’s largest species of grass—which may make this tranquil forest in Nanjing, Jiangsu, China, a beautifully manicured lawn. 
Photograph by Luis Marden, National Geographic

Discussion Ideas

  • Plants are often divided into three categories: annuals, biennials, and perennials. Browse through Carl Zimmer’s easy-to-read, fascinating blog post about bamboo life cycles. Do you think bamboo is an annual, biennial, or perennial?
    • Bamboo is a perennial, meaning it lives for more than two years. Most plants are perennials. Read this article to learn more about how one Nat Geo Explorer is working to make agriculture more sustainable through use of perennials such as switchgrass and sunflowers.
      • Biennials are plants that live for two years. In the first year, a biennial grows leaves, stems, and roots. In the second year, a biennial flowers, producing fruits and seeds. Onions and carrots are biennials.
      • Annuals are plants that complete their life cycle in no more than one year. Wheat and tomatoes are annuals.

 

Some species of bamboo flower every couple of years, while some only flower every 120 years. This bamboo is flowering in Inbamura, Chiba, Japan. Photograph by Joi Ito, courtesy Wikimedia. CC-BY-2.0.

Some species of bamboo flower every couple of years, while some only flower every 120 years. This bamboo is flowering in Inbamura, Chiba, Japan.
Photograph by Joi Ito, courtesy Wikimedia. CC-BY-2.0.

Chinese scientists and artists have been cataloging the life cycles of bamboo for more than 500 years. This spectacular scroll painting of finches on flowering bamboo branches was painted in the early 1100s by Huizong, an accomplished artist who had a nice day job as the Emperor of China. Ink on silk painting by Emperor Huizong, courtesy the Metropolitan Museum of Art

Chinese scientists and artists have been cataloging the life cycles of bamboo for more than 500 years. This spectacular scroll painting of finches on flowering bamboo branches was painted in the early 1100s by Huizong, an accomplished artist who had a nice day job as the Emperor of China.
Ink on silk painting by Emperor Huizong, courtesy the Metropolitan Museum of Art

 

  • According to The Loom, scientists “found that the [flowering cycles of bamboo] are tightly clustered around numbers that can be factored into small prime numbers.” What are prime numbers?
    • Take it away, Kevin Barnhart:
    • Prime numbers are positive numbers greater than 1 that cannot be divided evenly by any numbers besides 1 and themselves. (No negative numbers, no 0s, no 1s, no remainders, no decimals!) Take a look at the first 1,000 primes here.
      • Numbers that are not prime are composite: 4, 6, 8, 9, 10 . . . these are composite numbers, because they can be divided evenly by numbers other than 1 and themselves.
    • In this case, “small primes” probably means factors of 2, 3, and 5—the bamboo flowering periods studied can be broken down into factors of 2, 3, and/or 5.
    • Primes are fun:
      • Two is the only even prime, as every other even number can be divided by 2.
      • Five is the only prime number ending in 5, as every other number ending in 5 can be divided by 5.
      • If the numbers of a prime add up to a multiple of 3, that number can be divided by 3 and therefore is not a prime. (Example: 111 (1+1+1=3); 951 (9+5+1=15))
      • There are an infinite number of primes. Infinite! Browse through a few theories proving this, from 300 BCE to 2005.

 

  • What are some flowering periods that would fit the theory described in The Loom?
    • Think of composite (not prime) numbers: Bamboos that flower every 12 years, every 50 years, every 111 years, even 2,015 years would all fit this theory. Those numbers could all be factored down to small primes—and shorter-lived ancestors.

 

  • Why would a 120-year life cycle be more beneficial than a 1- or 2-year (annual or biennial) cycle? Read through the blog post and think about food webs in a bamboo forest.
    • According to Carl Zimmer, proving why he’s one of the best science writers around:
      • Rats, birds, pigs, and other animals devour colossal numbers of bamboo seeds. Each gobbled-up seed represents the loss of a potential [bamboo] offspring. If there are enough seed-predators, and they are hungry enough, they can wipe out a bamboo plant’s entire set of seeds.
        “Bamboo plants might fare better . . . if they flowered at the same time. They would overwhelm their enemies with food. Even if they gorged themselves to bursting, they would still leave some seeds untouched. Those surviving seeds would then have enough time to grow into plants that could defend themselves with tough fibers and bitter chemicals.”

 

  • If bamboo evolved to longer and longer life cycles, could some mutant bamboo go the other way and evolve shorter and shorter life cycles?
    • Not successfully. “If a four-year forest produces a two-year mutant, it will flower half the time in years when it has no protection from predators. The only direction it can go is towards longer cycles.”

 

TEACHERS’ TOOLKIT

Nat Geo: Bamboo Mathematicians

Nat Geo: What is quantitative data?

Nat Geo: Rat Attack in India Set Off by Bamboo Flowering

Kevin Barnhart: Prime Numbers Rap

The Prime Pages: The First 1,000 Primes

(extra credit!) University of Utah: Euclid’s Theorem (Why are there infinitely many prime numbers?)

One response to “Bamboozled by Prime Numbers

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s