Danielle,
Darlene,
Kellie,
Jill,
Nanyal,
Kevin,
Rachel,
Christina,
Jennifer,
Candice,
Vance,
Esther and
Melinda demonstrate calculations using distance formulas and equations of circles. A "Service Learning" Project to provide web pages for our community's better understanding of mathematics.

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. The South Tower is a composition of arcs that join on common tangent lines. The reason for the common tangent line is to have the arcs join in a visually smooth curve. At P35, P36, P37 and P38 the first derivative of the different arc curves match. The second derivatives do not match since the arcs have different radii at these points where they join.

We set out to find an equation of each arc and use inequalities or absolute value inequalities to specify the x and y values used in that arc.

The red line from P8 to P36 is the radius of the arc between P36 and P37.

The center point is P8 (340.0209,-48.92).

To get the arc for points P36 to P37 we used the equation of a circle:

(x - 340.00209)² + (y + 48.92)² = 23,651.548.

The arc radius is the square root of 23,651.548 which is 153.7906777.

For P36 = (479.4045, 16.07065) to P37 = (479.4045, -113.9107) points in the arc equation above we need to take y values such that:

Do the same process for the arc with center P9 between P35 and P38 to get:

p9 was our point

-113.9107 __<__ y __<__ 16.07065

the arc points were P35 and P38

the distance between P35 and P9 was 153.790768

here is the equation:

(x - 489.9792)² + (y + 48.92)² = 153.790768² = 23651.6003

Then take center point P7 for arc between P35 and P36 and calculate:

We used P7 as the center point to find the distance to P35 & P36. The equation, assuming we chose a point (x,y) that is on the arc being measured, is the square root of (x-x7)² + (y-y7)² = r². Where r = the distance of the arc's radius.

(x - 415)² + (y + 13.96167)² = 71.06251²

350.5955 __<__ x __<__ 479.4045

So with center P6 for arc through P37 and P38 we have:

The center point that on the circle is P6.

From P6 to P37, the distance was 71.062527.

From P6 to P38, the distance squared is also 71.062527.

Then the formula for this arc of the circle:

(x - 415)² + (y + 83.87833)² = 71.062527²

where 350.5955 __<__ x __<__ 479.4045

Student _________

I thought the Millennium hotel was a fascinating structure. I had no idea all the details that went into the planning of this hotel. I liked the part of the building that resembled airplane wings. I may have to go eat dinner there and show people what a neat building it is. Thanks for going "around" there.

Student _________

I loved the experience I had at the Millennium hotel.
It was beautiful. I especially liked going up to the
27th floor to the restaurant where Danielle and I were
greeted by a lovely African American Hostess who was
very nice. She welcomed us to go into the restaurant
to experience the movement. We watched the dinning
area as it moved and still couldn't believe it.
However, we thought that the whole top floor moved, so
we were kind of surprised when we found that it
didn't. Well, we had fun walking in the dinning area
in the opposite direction while it was moving.

Student _________

I had no idea that only a section of the
floor in the restaurant revolved. When I heard that
it was called the "revolving restaurant", I expected
the whole top level to move. When I went up to see
the revolving wonder, I realized that only a section
of the floor moves. It was very cool.
When I stepped on the moving floor I was delighted.
It moved very slowly, but still made me feel a little
dizzy. I don't know if I would be able to sit down
and eat dinner while I'm moving, but I would sure like
to try it sometime.

Student _________

The Millennium Hotel really did amaze me. I liked seeing different types of arcs and circles in the Hotel’s architecture and it
had many different themes in it's structure. I would
find it interesting to know how long the planning and took before the actual structure was built?
Another very interesting aspect was the revolving
restaurant, "Top of the Riverfront" located at the top
floor of the Millennium Hotel- St. Louis. The revolving
restaurant surprised me because when you are standing
in the restaurant moving, you are not just moving
straight but in a circular motion and as you move
around and sit and eat dinner, you can see some of
St. Louis' most famous landmarks all in 1½ hour meal sitting. I encourage everyone who has never
visited the Millennium Hotel in St. Louis to do so! It is
an experience worth taking!

Student _________

The Millennium Hotel was pretty cool. It really is an architectural marvel. It was neat how even the indoor pool fit into the design. It was ingenious of the architects to cut the work in half by using symmetry. I have had fun there on a couple of occasions for formal events, but we saw parts of the hotel I had not seen before and that made it more interesting.

Student _________

The one specific thing that sticks out in my memory is the pool at the hotel. The hotel is a circular structure. The pool is the shape of 1/4 of a circle. I'm not sure if this was done for that reason or if they had to do it because they didn't have a lot of space.