Spirals: Significance and Application

Main Assignments


Navigation:
Home
History
Polar Coordinates
Archimedean Spiral
Logarithmic Spiral
Significance and Application
Practice
Work Cited

Spirals are used all throughout pop culture. As seen below in Spider-Man: No Way Home, Peter recognizes that the mirror dimension is just a spiral! They can also be seen in season 7 of The 100, Arrival, the Divinci Code and more!


Archimedian Spirals

  1. Used as a more accurate measurement of the area of a circle, measuring the circumference with limited tools. The spiral allowed better measurement of a circle's circumference and thus its area, until later when a better approximation for Π was created

  2. Scroll compressors

  3. Antennas

  4. Watch springs

  5. Some Vinyls; although it wasn't stated specifically if they use an Archimedean Spiral or logarithmic

  6. Digital light processing

  7. Food microbiology

  8. Rotors

  9. One of its most interesting uses is when doctors ask patients to draw an Archimedean spiral, and then use that spiral to quantify human tremors.


Logarithmic Spirals

These spirals are often observed the most throughout nature.
  1. The path of an eagle to its prey or an insect to a light source

  2. Shell of a snail

  3. The arms of galaxies

  4. Weather patterns such as tropical cyclones or hurricanes, thus allowing meteorologists to predict the path, speed, and circular motion of the storm

  5. Plant formations

  6. Mechanically as spiral bevel gears

  7. Nerves of a cornea



Fun Facts

  1. Bernoulli had a spiritual endearment with the logarithmic spiral and believed that it would provide a symbol of hope for the resurrection of the dead at the end of the world.

  2. The first person to utilize polar coordinates was Bonaventura Cavalieri when he used them to solve a problem relating to the area within the Archimedian Spiral

  3. Leonardo Fibonacci came up with the Fibonacci sequence when calculating the ideal expansion pairs of rabbits over the course of one year

  4. If you look at the Fibonacci Sequence the third term of the sequence is 2 and every third number after that is a multiple of 2. Thus when n = 6: $$x_{n} = 8$$ When n = 9: $$x_{n} = 34$$


Now wake! You may not have been out for long but you sure absorbed a lot of information. Lets see if that hypnosis really worked shall we?