A Shoshone pine nut winnowing basket (photo from ISU
museum). Its shape is specifically designed for the winnowing motion. We can think of the rim of the winnowing basket as a rose-petal shape, pointed at one end and broad at the other. The wild rose is an important plant in Shoshone culture.
A common way to make such petal shapes in mathematics is by graphing in polar coordinates. The polar coordinate system is very similar to the Shoshone basket-making technique:
|Note that mesh inside the
basket originates from the many struts attached to the pointed end of the
petal. In the same way, the polar coordinate system always has the radius
attached to the origin point.
Here is a polar graph of
the function radius = cos(2*theta)+0.8. Shoshone basket makers have to
figure out how long each strut would be for each angle theta, just as the
function tells you the radius for each theta value.
|Now lets make a winnowing
basket! Go to the simulation window and experiment with the following parameters:
Use the mouse to change a value, then hit "enter" (you may have to do that more than once, check to see if the cursor is changed to an hourglass, if so just wait).
Try to see how close you can get the simulation to look like the original.
Try to create a totally new shape of your own design.
To save the image, left-click
on it and "copy."