Oval Not Elliptical Math Projects

P8 (340.0209, -48.92)           P9 (489.9792, -48.92)           P7 (415, -13.96167)
P6 (415, -83.878333)           P12 (415, -48.92)           P35 (350.5955, 16.07065)
P36 (479.4045, 16.07065)           P37 (479.4045, -113.9107)           P38 (350.5955, -113.9107)
P39 (492.9, -162.6)           P43 (339.02, -18.92)           P44 (341.02, -10.92)
P28 (322.2436, 54.08855)           P41 (292.162, -10.59464)           P30 (307.343, 22.04857)
P42 (301.2294, -14.81154)           P45 (332.051, -10.17386)           P46 (313.0053, 11.69534)
P47 (315.9571, 18.04252)           P48 (330.7162, 49.77843)           P29 (314.7933, 38.06856)

The oval shape of Four Points by Sheraton St. Louis Downtown (Millennium Hotel) is not an ellipse. As in the ballroom design the South Tower is a composition of arcs that join on a common tangent line. The reason for the common tangent line is to have the arcs join in a visually smooth curve. The first derivative of each curve match. The second derivatives do not match since the arcs have different radii at the point where they join.

The red line from P8 to P36 is the radius of the arc between P36 and P37. Find the equation of this arc and use inequalities or absolute value inequalities to specify the x and y values used in this arc. Do the same process for the arc with center P9 between P35 and P38, center P7 for arc between P35 and P36, and center P6 for arc through P37 and P38.

Use symmetry, areas of sectors, and areas of triangles to determine the area of the South Tower.

With thanks to the following college algebra students: Justin Cornish, Erin Cox, Steven Dodson, Kelly Fain, Kyle Flieg, Jeremy Freeman, Tiffany Gregorczyk, Kevin Kalinowski, Gabriel Keller, Joseph Koepke, Mary Lang, Christine McCarty, Joel Pattie, Nathan Remer, Pamela Roth and William Shaus on their Regal Riverfront Hotel graphs and calculations.

A "Service Learning" Project to provide web pages for our community's better understanding of mathematics.

Danielle, Darlene, Kellie, Jill, Nanyal, Kevin, Rachel, Christina, Jennifer, Candice, Vance, Esther and Melinda demonstrate calculations using distance formulas and equations of circles.

Millennium Hotel St. Louis/Four Points by Sheraton St. Louis Downtown Math Projects