This type of graph allows the student to
compare functions on the same axes. This example shows the first This particular example illustrates an interesting piece of history. In 1769,
James Bernoulli asserted that every function could be written as the sum of an infinite trigonometric series.
The famous mathematician Leonhard Euler said that this could not be correct. His argument was this:
there are discontinuous functions (like the sawtooth function shown here), but the trigonmetric functions
are continuous, and sums of continuous functions are continuous, so how could you get a discontinuous function
by adding up continuous functions? The graph above shows how! In MathXpert, you can use the If Euler had had MathXpert, he wouldn't have made this mistake, and the knowledge of such series would not have had to wait for Fourier's 1807 publication. |