Logarithmic spirals… Geometry… Trigonometry… If I told you these things are beautiful would you believe me? Or would you have visions of high school textbooks and exams that made you cringe?
Each time I see the exquisite beauty of dew on a spider’s web, I am awed that such a little creature can create a mathematical masterpiece!
Engineers and scientists have studied spider webs, and the silk they are made from, to learn the secrets of their beauty, strength, and flexibility.
Some amazing spider web facts:
Spider silk is
- lighter than cotton.
- more elastic and waterproof than silkworm silk.
- 1,000 times thinner than human hair.
- five times stronger than steel of the same diameter.
- It can stretch four times its original length.
One spider in Madagascar is known to form the world’s largest spider web with a dragline of up to 25m!
As well as the spider silk being a biological wonder, the construction of the web itself is also incredible. The Orb’s web has intricate geometry, and the angles and placement of the silk optimize the flexibility, strength, and economy of silk. The circular shape of the logarithmic spiral gives maximum strength and surface area with the minimum amount of silk. The spider tensions the lengths of silk, spinning and placing each thread in a beautiful pattern, reflecting trigonometric precision.
The amazing properties of spider silk and incredible web design have inspired architects, engineers, and scientists to look to the spider to help solve problems and inspire inventions. When a scientist looks to the design found in nature and uses this to inspire innovation we call this biomimicry. One area where spider silk is being used to advance engineering is in the nanotechnology field. By taking a strand of silk, as thin as 10 nanometers, and coating that in a chemical solution, scientists have found a way to create tiny hollow nanotubes. These tubes are used in fiber optics as tiny test tubes and in specialized microscopes.
If you want to learn more about biomimicry, the book Discovery of Design by Donald DeYound and Derrik Hobbs is a great place to start.
Have fun with your older students with this lesson from Intermathematics titled ‘Weaving a Spider Web’ They use advanced algebra and trigonometry to create a graphic illustration of a spider web.
For the younger students, you might like to go on a walk to discover spider webs.
- Take a water spray bottle with you and lightly spray the web so it’s easier to see.
- Discuss the different shapes you can see.
- Take a photo of the web.
- When you get home enlarge and print the photo.
- Using a bright pen, highlight the different parts of the web and measure the angles.
- Write about what you have discovered in your math journal.
Now relax and enjoy watching a spider weave its web!
