View Proposal #560
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| ID | 560 |
|---|---|
| First Name | Marshall |
| Last Name | Whittlesey |
| Institution | California State University San Marcos |
| Speaker Category | faculty |
| Title of Talk | Using quaternions to prove theorems in spherical geometry |
| Abstract | It is well known that the complex numbers can be used to do transformation geometry in the plane. In particular, rotation by angle ϴ about the origin is accomplished via multiplication by the complex number e^iϴ=cos ϴ+ i sin ϴ. It is less well known that the quaternion algebra (consisting of expressions of the form a+bi+cj+dk with i^2=j^2=k^2=ijk=-1) can be used to do similar transformations in three dimensional space. In this talk we show how to use quaternions to prove an interesting classical theorem in spherical geometry. These methods are featured in the speaker's new book with CRC Press, "Spherical Geometry and its Applications", which the author hopes will be attractive for use in topics courses in geometry. |
| Subject area(s) | Geometry |
| Suitable for undergraduates? | Y |
| Day Preference | SaturdayMild |
| Computer Needed? | |
| Bringing a laptop? | |
| Overhead Needed? | |
| Software requests | |
| Special Needs | |
| Date Submitted | 09/15/2021 |
| Year | 2021 |