A Voluminous VesselA Project in Student Creativity and Faculty

CollaborationBrenda Edmonds

Rob GrondahlCathleen O’Neil

Johnson County Community CollegeOverland Park, KS

Hmmm…Extending beyond the textbook

Different types of applications Mathematics is creativeMathematical communication

Brenda found “The Mathematical Guzzler” by Steven Kifowit, Prairie State College, Chicago Heights, IL

Project D01 - The Mathematical Guzzler

For this project, you will design a beer glass by defining a function y = f(x) and rotating its graph about the x-axis to form a surface of revolution. Your design is subject to the following constraints:

the glass must hold 1-1.5 pints;

the base must have a diameter of 2-3 in;

the top (opening) must have a diameter of 3-3.5 in;

the height must be 5-7 in;

the defining function y = f(x) must have a continuous, non-constant derivative throughout its domain; and

the defining function cannot be a polynomial.

You can be very creative in defining your beer-glass functions, but be careful to satisfy the constraints….

1. Define a beer-glass function that satisfies the constraints listed above. Show that each constraint is satisfied.

2. Sketch a detailed graph of the function.

3. Write a paragraph that clearly describes your beer glass design. Write for a person with no knowledge of mathematics. Use correct grammar and spelling!

4. Sketch a detailed drawing of the beer glass you obtain by rotating the graph of your beer-glass function about the x-axis.

5. Set up the definite integral that gives the lateral surface area of your beer glass. Use your calculator or CAS to approximate the value of this integral.

6. Combine your results and ideas from problems 3 and 4 to make a “poster” advertising your design. It doesn't need to be a huge poster, an 8'' by 10'' poster will work just fine.

http://stevekifowit.com/class_archives/projects/d01.htm

The Voluminous Vessel ConstraintsYou will use metric units (cm) for your functions.The glass must be between 10 and 30 cm tall.The diameter of the base of the glass must be

between 5 and 12 cm.The opening at the top of the glass must have a

diameter between 7 and 10 cm.The thickness of the glass at the top must be more

than 0 cm and less than 0.5 cm.The functions that define the inside and outside

surfaces of the glass must be continuous and have non-constant derivatives throughout the necessary domain.

Evolution of the ProjectAn evaluation rubric was developed

Cathleen added a student collaboration component

Some class time to work and get feedback

Requiring a draft (or two)

Giving some examples

Final Project is a Written ReportIntroduction of the problem to the reader. (This

“problem statement” will also contribute to demonstrating your understanding of the problem.)

Equations for the functions that define the outside and inside of the glass, with appropriate restrictions on the variables.

Diagram showing the functions revolved about an axis to create the glass.

Set up of an integral (using correct mathematical notation) to find the volume of the material needed to create the glass, and approximated value of the integral labeled in appropriate units.

Set up of an integral (using correct mathematical notation) to find the volume of liquid the glass will contain when filled, and approximated value of the integral labeled in appropriate units.

Set up of an integral (using correct mathematical notation) to find the surface area of the outside of the glass, and approximated value of the integral labeled in appropriate units.

Evaluation of your glass design. Include a discussion of what criteria you used to evaluate the design.

Separately, an evaluation of your own and your group members’ collaboration using a rubric.

EvaluationFirst Draft (5 points)Final Draft (40 points)

Neatness, Organization, Grammar (6 points)Understanding of Problem (5 points)Definition of Equations (5 points + 1 extra

credit)Diagram(s) (5 points)Integrals and Approximations (15 points)The Difference Between Good and Great (4

points)Collaboration (5 points)

From Design to ProductionThe value of hallway conversations and

faculty collaboration10 points extra credit for creating an .stl

file

A Beauty Contest Winner

Students WANT to Do Work?!?“Are we going to do that project?”Rob figured out that Mathematica can export as an .stl file

RevolutionPlot3D and Show commands in Mathematica

Student sales pitches

http://blogs.jccc.edu/rgrondahl/voluminous-vessel-project/

Finally+DoneMATH+242-002+Project+1+--+Markovich,+Sabha,+Sweden.docx

Our design for the medieval chalice is true to all of the original requirements of the project. It is visually regal and elegant to behold. The vessel is very usable, as it will hold a reasonable volume of liquid beverage. The goblet is also ergonomically practical, as the user can either grasp the stem in one hand or cup the upper bowl in both palms comfortably. Within the constraints of the project, our team was able to design a drinking vessel that is practical, beautiful, and fit for a royal court out of a medieval legend.

http://blogs.jccc.edu/bedmonds/files/2015/10/BrendasGlass.pdf

Wait, we have to write a paper too?!?http://blogs.jccc.edu/rgrondahl/files/2014/11/Sample-Vessel-Project.pdf

What I like about this project…Mostly we have future engineering majors –

they love doing something that feels real.They get to know some other students in the

class. They work way harder on it than I expect.They learn math for this project that is

beyond the basic curriculum for the course.They learn how to use some useful software.They are excited.Other students get interested in learning

more math.

More InformationBrenda Edmondsbedmonds@jccc.edu

blogs.jccc.edu/bedmonds

Rob Grondahlrgrondahl@jccc.edu

blogs.jccc.edu/rgrondahl

Cathleen O’Neilconeil@jccc.edu