Hello again;
If we could get rid of hours and minutes and seconds as well
as the 360 degree circle I would also get rid of the math we
use to measure round things.
I am a house designer and I noticed that a larger house is
cheaper to build per square foot than a similar shaped
smaller house. This is because the exterior walls are one of
the most expensive parts of the house.
For example:
A 10' x 10' house has 100 sq.ft.
It has 40 linear feet of exterior wall.
If 1 linear foot of wall cost $10, the exterior walls would
cost $400 or $4 a square foot of floor space.
vs:
A 100' x 100' house has 10,000 sq.ft.
It has 400 linear feet of exterior wall.
1 linear foot costs $10, the exterior walls would cost
$4,000 or 40 cents a square foot of floor space.
I noticed further that different shapes are more efficient
than others if you look at exterior walls vs. floor space.
For example:
A square house 100' x 100' has 400' of exterior wall and
captures 10,000 sq.ft. of floor area.
vs:
A rectangular house 150' x 50' has the same 400' of exterior
wall but captures only 7,500 sq.ft. of floor area.
It turns out the circle is the most efficient shape as its'
exterior wall captures the most floor space.
To reduce it to basics, a one inch square captures 1 square
inch with a perimeter of 4 inches.
A circle with the same perimeter/circumference of 4 inches
captures 1.27 square inches, the ideal line efficiency.
I also noticed that the number 1.27 is useful to calculate
areas of circles without using Pi. Simply take any
circumference and divide it by 4 and then square the result,
essentially turning the circle into a square. Next, simply
multiply that square area by 1.27 for the area of the circle
without using Pi.
The problem with 1.27 is I had to calculate that using Pi,
so it is also one of those never ending numbers like Pi.
It can be calculated by dividing 4 by Pi =
1.27323954473516...etc.
I'm not very comfortable with this number. The reason is a
round house has an exact floor area but I can never
calculate it. I always get an approximate answer that I have
to round off.
The problem here seems to be our math system is not very
good for calculating round things. Our system works great
for counting things; 12 dinosaurs, 3 eggs, 22 shells and
great for measuring the area of things that are enclosed
with straight lines but totally lacking when it comes to
measuring curves or the area of round things.
That's why I propose a new round math for doing this.
I would start with a circle with a circumference of 4" and
call the area of that circle 1 "round" inch instead of 1
square inch.
Now to do the area math on a few circles I would just divide
the circumference by 4 and square the result for an answer
in "round" inches:
circle #1: circumference = 12"
12/4 = 3
3x3 = 9 round inches
circle #2: circumference = 20"
20/4 = 5
5x5 = 25 round inches
Now I can add them together easily:
25 + 9 = 34 round inches
or any other math functions and will get results in "round"
numbers. You can now easily calculate round areas "exactly".
If you then want to convert the round numbers back to square
numbers for some reason, simply multiply by my 1.27323954473
I would think it would be useful in calculating huge round
things like the orbits of planets where even a small error
can have big consequences. By calculating "round" numbers
you will get "exact" results.
And besides that, it would be simple to measure round things
without using clumsy Pi, that never gives you the right
answer anyway.
brent
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