delimathsphere

Deli Tray Math Sphere

Plot a sphere in 3 dimensions

Introduction

Transparent trays used in delis to serve salads stack together in transparent layers which can be used to show contour maps of three dimensional shapes.

A contour map of a sphere.

Material

10 deli salad containers, transparent
scissors
tape or double sided tape
Sharpie, or other marker to write on plastic.
Contour maps of mathematical shapes in 3-D(Created by various programs like Graphing Calculator)

Assembly

Cut the bottoms and tops of the deli containers apart. Set aside the tops of the containers they can be used as well but you should always use tops with tops and bottoms with bottoms.

Use a mathematical plotting program to draw the contour map of a three dimensional shape such as a sphere.

For example a sphere z = (x^2 + y^2)^1/2

Print the contour map out so that the largest contour will fit inside the flat bottom of a deli container.

Tape the paper copy of the contour map to the bottom of one deli container using 4 loops of tape, one loop at each corner of the deli tray(or double sided sticky tape) the tape will keep the contour lines in position with respect to the deli tray.

Drop an empty deli tray into the deli tray that has been taped to the paper master.

Use a sharpie to trace the lowest contour line onto this deli tray.

(To erase mistakes use rubbing alcohol and a q-tip)

Label this deli tray #1 and set it aside.

Place another deli tray into the deli tray that has been taped to the paper master.

Use a sharpie to trace the next lowest contour line onto this deli tray.

Label this deli tray #2 and place it inside deli tray #1.

Repeat for all 9 contour lines.

To Do and Notice

Keeping the stack of 8 trays together look at the contour lines of the function in three dimensions.

Turn it over and look at the bottom.

Notice you have made a three dimensional map of a shape.

However perhaps the sphere is not spherical, mine was squashed into an ellipsoid of revolution. This is because the spacing of the contour lines in the z direction may not be equal to the spacing in the x and y directions.

For min I needed to either adjust the contour lines on the drawing of the sphere by making the sphere a smaller diameter. Or increase the spacing of the deli trays.

I chose to increase the spacing of the deli trays by cutting soda straws into 2 cm (1 inch) long segments and taping four of then to the inside corners of each tray.

This increased spacing made the ellipsoid more spherical.