View Proposal #144
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| ID | 144 |
|---|---|
| First Name | Dave L. |
| Last Name | Renfro |
| Institution | ACT Inc. |
| Speaker Category | other |
| Title of Talk | The Remarkable Equation tan(x) = x |
| Abstract | Although tan(x) = x is virtually the prototypical example for solving an equation by graphical methods, and this equation frequently appears in calculus texts as an example of Newton's method, there seems to be nothing in the literature that surveys what is known about its solutions. In this talk I will look at some appearances of this equation in elementary calculus, some appearances of this equation in more advanced areas (quantum mechanics, heat conduction, etc.), the fact that this equation has no nonreal solutions and that all of its nonzero solutions are transcendental, and some curious infinite sums involving its solutions. In addition, I will discuss some of the history behind this equation, including contributions by Euler (1748), Fourier (1807), Cauchy (1827), and Rayleigh (1874, 1877). |
| Subject area(s) | transcendental equations |
| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | |
| Bringing a laptop? | N |
| Overhead Needed? | Y |
| Software requests | No |
| Special Needs | None |
| Date Submitted | 3/27/2006 |
| Year | 2006 |