Assignment 22 — functional chrestomathics

Due Monday, April 5

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Module beanery.py (code will be available at the start of class)

• The module defines three functions volume(), count(), and guess().

• A simple tester yum.py for the functions is provided.

• None of your functions should get input or print output.

• Examine and think about algorithms for the problems. However, do not write any code before class.

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Function volume( a, b )

• Returns the volume of jelly bean with length a and height b.

• Based upon hours of research, zillions of jelly beans, and a bunch of mason jars, it has been concluded that the volume of a jelly bean can be roughly modeled as the average of the volume of the exterior bounding cylinder and of the volume of the interior bounding ellipsoid.

• Our formula for the volume s of a single jelly bean is:

• To make your calculation as accurate as possible, use Python's math module constant math.pi to estimate π when needed.

• A run of of the tester should produce output

volume( 1.3 , 0.7 ): 0.41691552507014545

volume( 2.0 , 1.0 ): 1.3089969389957472

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Function count( s, j, f )

• Returns the number of beans that can fit in a jar with volume j, given the loading capacity is f and the size of a bean is s.

• The count formula is: ⌊ j × f / s ⌋, where the ⌊ ⌋ operators are the mathematical symbols for rounding down to the nearest integer; that is, for a positive number dropping the fractional amount.

• A run of of the tester should produce output

count( 0.42 , 125 , 0.7 ): 208

count( 1.31 , 500 , 0.6 ): 229

• Questions

• What built-in function converts a decimal to an integer?

• Should function volume() be helpful?

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Function guess( a, b, j )

• Returns the number of number jelly beans with length a and height b that can fit in a jar with volume j. Exhaustive research has determined the jelly bear jar loading factor is typically 69.8% (i.e., .698).

• A run of of the tester should produce output

guess( 1.3 , 0.7 , 125 ): 209

guess( 2.0 , 1.0 , 500 ): 266

guess( 1.52 , 0.9 , 1550 ): 1342

• Questions

• Should function volume() be helpful?

• Should function count() be helpful?

 

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