Booth Id:
MATH026T
Category:
Mathematics
Year:
2017
Finalist Names:
Na Ranong, Napob (School: Tesoro High School)
Thanyacharoen , Kasidetch (School: Paradise Valley High School)
Theerakiatsakul , Ratthee (School: Campolindo High School)
Abstract:
In this project, we defined a mid-tangent point with respect to a fixed point X and a tangent at a point P on planar curve C as a point on the tangent that is equidistant from X and P. We studied the locus of mid-tangent points of conic sections. We found that the locus of mid-tangent points of most conic sections are non-linear curves. However, we observed and proved by using Euclidean geometry that the locus of mid-tangent points of circle is straight lines. The mapping defined by mid-tangent points was studied further. The similarity between a mid-tangent projection and a stereographic projection was displayed as a one – to – one correspondence function. We also extended the concept of mid-tangent points to three-dimensional space and found that the similarity with the stereographic projection was retained in higher dimensions. Finally, we applied the locus of mid-tangent points of a sphere to create any specified region; e.g., creating maps of Thailand and California.