EQUATIONS AND FORMULAS FOR THE

Planetarium Information

ST. LOUIS SCIENCE CENTER PLANETARIUM

HYPERBOLOID OF ONE SHEET, HYPERBOLA:

x2/930.25 - y2/237.16 = 1

FOR:   -85 ≤ x ≤ -30.5   or   30.5 ≤ x ≤ 85   and   -40 ≤ y ≤ 14.5

SKY DOME:

y = (39.37012 - x2)½ - 38.125

FOR:   -39.3701 ≤ x ≤ 39.3701

LEVEL A       SERVICE AREAS:

y = -61.5

FOR:   -100 ≤ x ≤ 100

LEVEL B       EXHIBIT AREA AND OUTSIDE WALKING RING:

y = -48

FOR:   -80 ≤ x ≤ 80

LEVEL B       EXHIBIT AREA OUT SIDE WALL/WINDOW:

x = 70.5

FOR:   -48 ≤ y ≤ -32.373

LEVEL C       BOTTOM OF HYPERBOLOID OF ONE SHEET:

y = -40

FOR:   -85 ≤ x ≤ 85

LEVEL D       HEMISPHERE EDGE:

y = -38.125

FOR:   -39.3701 ≤ x ≤ 39.3701

LEVEL E       RING EXHIBIT AREA:

y = -37

FOR:   -61.5 ≤ x ≤ -42   or   42 ≤ x ≤ 61.5

LEVEL F       HYPERBOLA'S TRANSVERSE AXIS:

y = 0

FOR:   -100 ≤ x ≤ 100

LEVEL G       TOP OF SKY DOME:

y = 1.2541

FOR:   x = 0

LEVEL H       ROOF TOP:

y = 7.5

FOR:   -33.9247 ≤ x ≤ 33.9247

LEVEL I       TOP OF HYPERBOLOID OF ONE SHEET:

y = 15
and:
y = 14.5

FOR:   -42 ≤ x ≤ 42

LEVEL J       TOP OF OBSERVATION DECK:

y = 17

FOR:   -12 ≤ x ≤ -3.75   or   3.75 ≤ x ≤ 12

LEVEL J       OBSERVATION DECK WALL:

x = 11.333

FOR:   8 ≤ y ≤ 17

LEVEL K       SKY DOME PROJECTOR CENTERED AT:

y = -38.125

FOR:   x = 0

LEVEL B-       UNDER LEVEL B OUTSIDE WALKING AREA:

y = -50.75

FOR:   -89.5 ≤ x ≤ -75.5 or   75.5 ≤ x ≤ 89.5

LEVEL P       PLAY GROUND EXHIBIT AREA:

y = -???? below (0, 0)

FOR:   x = ???? ± ?????   and   z = ???? ± ?????

IE FOR: x feet North ± ????? feet   and   z feet East ± ????? feet from center of hyperbola

      

You may like to rotate:

                          X = 30.5 ( 1 + Y^2 /15.4^2)^0.5 

           for -40 less than or equal to Y less than or equal to 14.5 

about the Y axis to get the general idea of what you see from
Highway 40.

This material is presented in tribute to Mr. Chih-Chen Jen, Mr. Albert Alpers, Mr. Milo Ketchum, and Mr. Thomas Teasdale. You may link to the following pages:

INTRODUCTION

HISTORY AND LOCATION

MATH PROBLEMS AND PROJECTS I.

MATH PROBLEMS AND PROJECTS II.

FIELD TRIP PICTURES

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