Math Gurus: Walking across my world

[WanderingMonster]

Mods: Question's been answered. Feel free to move this thread to a more appropriate forum!

Mods: Please keep this in General...I think high traffic will help get this sticky question answered. Thanks!

Dear Math Gurus,

I am creating a world of my own that exists on the inside of a celestial chalice. I want the surface area to be roughly earth-sized. Assume that the chalice is a hemisphere, and units are miles. Here's what I think I need to know:

• The radius of the sphere
• The circumfrence of the lip of the hemisphere
• The walking distance (along the inside of the hemisphere) from any point along the lip of the hemisphere, to the center (actually a point 90 degrees from point A.

Thanks ahead of time! I should have paid attention in school!

 

[Umbran]

If it is Earth-sized, and I recall my numbers properly:

1)Radius of the Earth = 6367km = 3956 miles

2)Circumference of lip = Pi * Diameter = Pi * 2 * Radius = 24,856 miles

3) 90 degrees of arc = 0.25*Circumference = 6214 miles.

 

[Ampolitor]

hmmmm

I believe the circumfrence is like 25,000 miles or around there somewhat. fractal terrains has all that info, Im at not at home so i cant get you the info just yet.

 

[Iron Sheep]

The relevant formula is the formula for the surface area of a sphere:

A = 4 * Pi * r^2

I'm not precisely sure of the dimensions of the Earth in miles, but let's say that the poster above is correct (it's in the right ballpark, at least). Then the surface area of the Earth is roughly 196 million square miles.

The radius of a hemisphere with the same surface area is then going to be about 5600 miles.

You can then calculate the distance between any two points on the hemisphere by the formula:

d = pi * angle/180 * r

where the angle is the angle between the lines from the centre of the hemisphere to the two points.

So the circumference is about 35000 miles, and the distance from the rim to the centre will be a quarter of that, or about 8750 miles.

Hope this helps.

Corran

(edit: missed an "r" in the distance formula)

 

[WanderingMonster]

Thanks you guys! I really appreciate it!

 

[Storminator]

Hey! So what's on the outside of the chalice?

PS

 

[LightPhoenix]

Hey! So what's on the outside of the chalice?

PS

Divine cooties.

 

[Rel]

Hey! So what's on the outside of the chalice?

PS

And does it rest on the back of a giant turtle?

 

[WanderingMonster]

Mods: Now that my question has been answered, please feel free to move this to a more appropriate forum. Thanks!

The outside of chalice is the Astral Plane. Since it is an actual divine chalice, the jewels which adorn it are actually color pools to the outer planes.

There is no giant turtle. Sorry!

 

[MeepoTheMighty]

That's gotta be a weird world to live in. Does the sun stay at a static point in the sky? What does the horizon look like with inverse curvature? On a really clear day, can you see the other side of the bowl?