Lots of math to get a nice house (floor, windows, rooms)

[caters]

If I were to build a circular house, perfectly circular, I would need to know 1 measurement above all others, the radius. But I do believe that for building the house or the rooms(in case I wanted the rooms to be circular as well) I would need to know 2 radii. 1 would be the inner radius and the other one would be the outer radius. And if I was wanting everything circular I would have to do all these calculations:

pi*r^2

pi*r^2*h

2pi*r

And if I wanted the total area of the rooms on any floor without any extra area I would have to do this complicated equation:


R = inner radius of whole house
r = inner radius of room

pi*R^2 - (pi*R^2 - SUM(pi*r^2))

That second term in parentheses represents the area not taken up by circles.

Is it possible to build a house that is perfectly circular and has perfectly circular rooms and have doors and windows have the same arc length as the section of the circle they take up without the risk of wedging doors into circular walls while making sure that the area that isn't taken up by circles is not too small or too large(basically finding a comfortable midpoint between too small of an area and too large of an area)?

[froglipz]

Why?

[caters]

I'm just asking, and partly because a character in my Math World story called Pi is building himself a house all based on circles.

Pi won't settle for triangles, squares, pentagons, or any other polygon. He wants circles and he is going to make sure he has circles and shapes based on circles(so like cylinders and spheres for example).

[LifeIsGood01]

The rooms would not be circular, they would have a round edge.

Depending on how thick you want the outer wall subtract those inches from the outer radius and you have the inner radius.

The Only way to have round rooms is to make round structures that are connected or to have empty space between each round room in a big round house.

[caters]

What do you mean? Couldn't they be circular and still be just as good of a house? Because, I mean, if I was like Pi. I would get frustrated if what I built wasn't circular or at least based on a circle somehow.

[LifeIsGood01]

These are the only 2 ways I can think of to make round rooms, the big circle one has a lot of wasted space. I did it fast but hopefully you get the point.

[caters]

See I was thinking something more along the lines of this:



An Apollonian gasket, except only the first and second and possibly third layers would be circles. Of course I would have to adjust the Apollonian gasket so that there is a convenient amount of area between the circles or have all doors open into the circle(doors opening into the circle would be better if area being too large between circles is a concern).

But someone like Pi would absolutely love this Apollonian gasket design because all the rooms would be circles within a circle.

[LifeIsGood01]

Originally Posted by caters

See I was thinking something more along the lines of this:



An Apollonian gasket, except only the first and second and possibly third layers would be circles. Of course I would have to adjust the Apollonian gasket so that there is a convenient amount of area between the circles or have all doors open into the circle(doors opening into the circle would be better if area being too large between circles is a concern).

But someone like Pi would absolutely love this Apollonian gasket design because all the rooms would be circles within a circle.

You could so that for a story, but in reality there would be wasted space between the circles.

If it was a story I wouldn't bog it down with math, just dimensions and explain the gaps between rooms, the larger ones outside of the main room could be closets.

[justanokie]

House shaped like elysium space station. Start with outer ring then have smaller and smaller rings until you get to a center spherical room.

[sheerbliss]

Could Pi live in a yurt, sandbag building or quonset hut?