hungry little caterpillar, eric carle

The Very Hungry Daderpillar Analysis

 

The Very Hungry Daderpillar Analysis

By Hugh Gallon

How much would a Hungry Dad eat, if he ate the equivalent of the Very Hungry Caterpillar? A  seemingly simple thought that occurred to me while reading a bedtime story to my two year old son . It resulted in two 3+ hour sessions, late into the night, adopting and abandoning multiple trains of logic/methodologies.  It required re-learning high school mathematics and analyzing the two dimensional pages of a great children’s book to assess the  three dimensional volume of illustrated food. 

Read and enjoy the below, because I am never getting that six 6 hours of my life back.

Methodology: Assuming our caterpillar eats approximately his own body’s circumference through the items’ width/thickness (a simple caterpillar-sized tunnel through the food), I used pi and math to determine volumes of the foods and the size and volume of an average man and likely caterpillar.  I reviewed the size, shape, of each food item in the book as well as the location and angle from which the caterpillar purportedly burrowed.
Result: The Very Hungry Daderpillar would eat (conservatively) 700 apples,1100 pears, 2100 plums, 3500 strawberries, 3600 oranges, 500 pieces of chocolate cake, 1300 ice cream cones, 1100 pickles, 3000 slices of swiss cheese, 6000 slices of salami, 6000 lollipops, 1400 slices of cherry pie, 1100 sausages, 700 cupcakes, 1000 slices of watermelon.
Research Questions Answer Source
What type of caterpillar is it? Parnassian larvae http://www.eric-carle.com/q-cocoon.html
What is the average weight and size of Parnassian Larvae? Length (inches) = 1.24 / Weight (grams) = 1.5 (or 0.00330693 lbs) /  Circumference (inches) = 1 / Diameter (inches): 0.31831 / Radius (inches): 0.159155  / Volume as a tube (cubed inches): 0.09868 Peterson First Guide to Caterpillars of North America; http://www.gardenswithwings.com/butterfly/Anise%20Swallowtail/index.html; http://www.canadiangeographic.ca/kids/animal-facts/monarch_butterfly.asp
What is the average size of a man? Height (inches): 69.3 / Weight (grams): 88677 (or 195.5 lbs) / Waist circumference (inches): 39.7 /  Diameter (inches): 12.63691 / Radius (inches): 6.318455 /  Volume as a tube (cubed inches): 8691.70346 /  Volume estimated (cubic inches based on water): 5 357 http://www.cdc.gov/nchs/fastats/body-measurements.htm   & http://www.aqua-calc.com/calculate/weight-to-volume/substance/human-blank-body
How much does the average caterpillar eat? Double its own weight each day. 1000x its own body mass in a lifetime. A history of the earth and animated nature, Volume 2 By Oliver Goldsmith; www.obsessionwithbutterflies.com/owb_caterpillar.html; http://insects.about.com/od/butterfliesmoths/a/10-Cool-Facts-About-Caterpillars.htm
How long does a caterpillar live 7-21 days http://www.answers.com/Q/What_is_the_lifespan_of_a_caterpillar
How many Days did the Very Hungry caterpillar eat? seven days (counting the leaf) The Very Hungry caterpillar, Eric Carle
The Math
Each item eaten by the Very Hungry caterpillar Diameter/ Thickness of item (inches) – this is the length of the hole eaten through by the caterpillar for each item Estimated volume of item (cubed inches) Ratio of self eaten by caterpillar for a single item (thickness of item divided by 1.24 inch length of caterpillar) Ratio of self eaten by caterpillar for a cumulative # of item eaten Volume eaten by caterpillar = volume of caterpillar (0.09868 cubed inches) times ratio of self eaten in cubed inches
apple 2.75 16.3544 222% 222%               0.22
pears 2 16.354 161% 323%               0.32
plums 1.75 10.90 141% 423%               0.42
strawberries 1 5 81% 323%               0.32
oranges 2.75 16.3544 222% 1109%               1.09
chocolate cake 3 27 242% 242%               0.24
ice cream cone 2 6.685 161% 161%               0.16
pickle 1 4 81% 81%               0.08
slices of swiss cheese 0.125 0.18 10% 10%               0.01
slices of salami 0.125 0.09 10% 10%               0.01
lollipop 0.125 0.09 10% 10%               0.01
slices of cherry pie 3 9 242% 242%               0.24
sausage 1 4 81% 81%               0.08
cupcake 4 25 323% 323%               0.32
slice of watermelon 1 4.5 81% 81%               0.08
The Math
LOW ESTIMATE Volume eaten by human using volume of human if he eats a circumference equal to approximately with his actual volume (5357 cubed inches) times ratio of self eaten in cubed inches HIGH ESTIMATE Volume eaten by human using volume of human if he eats a tunnel of food as wide as his diameter (8691.7 cubed inches) times ratio of self eaten in cubed inches LOW ESTIMATE number of items a human would eat to be equivalent to the very hungry caterpillar HIGH ESTIMATE number of items a human would eat to be equivalent to the very hungry caterpillar
      11,880.44         19,275.96  700 apples  1200 apples
      17,280.65         28,037.75  1100 pears  1700 pears
      22,680.85         36,799.55  2100 plums  3400 plums
      17,280.65         28,037.75  3500 strawberries  5600 strawberries
      59,402.22         96,379.78  3600 oranges  5900 oranges
      12,960.48         21,028.31  500 pieces of chocolate cake  800 pieces of chocolate cake
        8,640.32         14,018.88  1300 ice cream cones  2100 ice cream cones
        4,320.16           7,009.44  1100 pickles  1800 pickles
           540.02              876.18  3000 slices of swiss cheese  4900 slices of swiss cheese
           540.02              876.18  6000 slices of salami  9700 slices of salami
           540.02              876.18  6000 lollipops  9700 lollipops
      12,960.48         21,028.31  1400 slices of cherry pie  2300 slices of cherry pie
        4,320.16           7,009.44  1100 sausages  1800 sausages
      17,280.65         28,037.75  700 cupcakes  1100 cupcakes
        4,320.16           7,009.44  1000 slices of watermelon  1600 slices of watermelon