# Episode #01: Geofront Geometry

(Expanded Commentary from C-168)

MDWigs: The Geofront is a sphere with a diameter of 13.75 km). However, 89% of it is buried and only the top part (900 m high and 6 km across) is open. I'm not sure if those figures are internally consistent; using geometry, you can work out if a sphere with a diameter of 13.75 km can be intersected to produce a top section 6 km across and 900 m high, and that could also be checked with the 89% figure.

Mr. Tines: The figures aren't at all consistent, I'm afraid. Dusting off the high-school maths, we have:

• Center of sphere to top of sphere = radius of sphere = 6.875 km (by definition)
• Top of sphere to Geofront ground level = 0.900 km
• Centre of sphere to where Geofront ground level touches = radius of sphere = 6.875 km (by definition)
• Centre of sphere to Geofront ground level = 5.975 km
• There is a right angle triangle centre of sphere/Geofront ground level above centre (where the right angle is)/ground level touches sphere.
• So Pythagoras gives 6.875² = 5.975² + (radius of geofront ground level)², i.e.