Using Math to Build My House
Jeff Goodman
goodmanjm@appstate.edu
Planting Trees: How many in 10 acres?
What do we need to know?
A. How closely should the trees be planted?
1 tree every 6 feet in each direction.
B. How big is an acre?
220 yards by 22 yards = 4840 square yards.
So, we can
get 11 x 110 =
1210 trees in
an acre, or
12,100 trees
in 10 acres.
How long a log for a rafter?
What do you need to know?
8ft
10:12 pitch – goes up 10” rise for every 12” of run
80”
125”
896”
ft
802 + 962 = (rafter length)2
David is making two cuts on a large piece of wood.
He’s going to cut a 2” thick piece and a 1” thick piece off and leave an 8” beam.
How thick should the beam be before the cuts, if the blade takes out 1/8th of an inch
On each cut?
8 + 2 + 1 + (2 x 1/8) = 11 ¼
Remember,
each cut
removes 1/8”
of wood.
He’ll make another cut that is 1” thick, leaving 8” behind.
1”
2”
How thick
should the
whole piece
be?
Let’s estimate to see if he did this right.
$170 x 5 = $850
We have almost this many 1000 board feet of 1” boards.
50
225
250
90
Calculating acreage
80,000 ft2
43,560 ft2/acre
How many yards of sand do I need to mix mortar for this wall?
Let’s see. A bag of
cement is 1 cubic foot,
and a “yard” of sand is
really a cube of sand one
yard on a side (yd3).
I have 18 bags of cement.
Mortar Mix 1:3
cement
sand
18 ft3 of cement
would require
18 x 3 = 54 ft3 of
sand.
And a cubic yard of
sand is 27ft3. So I
need to order 2 “yards”
of sand.
3 ft
3 ft
3 ft
Cubic yard
?
26 ½
28 ¼
28 13/16
3 ½”
What’s the total length?
33 1/16 + 3 ½ = 36 9/16
How wide
is one
board?
1¾
$597.65
=?
$597.65
x .7x=.7$418.36
Try it in your head: estimate!
What
information
is necessary
to define
these
shapes?
What’s the best way to define these curves?
Roofing!
What is the angle here?
What math is behind a set of stairs?
For stairs to be comfortable, they should be proportioned by the formula:
2 x (riser height) + (tread length) = between 24 and 26 inches
RISERS
I got 3 rises out of a set of triangular (turning) steps at the bottom
RISERS
With 10 more rises on the straightaway, I would have 13 rises total.
RISERS
My total height was 8’ 6 ¾” so each of 13 risers would be
102.75/ 13 = 7.9
= a little less than 7 29/32
TREADS
I had 8 feet of floor space to put in 10 stairs on the straight run
TREADS
So the tread for each stair would be:
968inches
feet / 10 = 9.6 inches per stair
= a little more than 9 19/32
How did I do with the formula for comfort?
2 x (riser height) + (tread length) = between 24 and 26 inches
Risers = 7.9 inches
Treads = 9.6 inches
(2 x 7.9) + 9.6 = 25.4
Must go somewhere…
Sink drains into the bowels of the earth
3” x 2” x 3” Y
What is the
naming
convention for
T’s and Y’s?
2” x 1 ½” x 2” T
A waste pipe should be
sloped 1% - 2%. How
much should it slope per
foot?
x
=.01
12
x =.12
I know that 1/8” is .125”, so a
1% slope is a little bit less than
1/8 inch per foot.
A cord is a 4’ x 4’ x 8’ stack
We burn about 3 cords of wood a year to heat our house.
Remember, we need 3 cords (each 4’x4’x8’) for the winter.
Approximately what fraction of our yearly supply of wood is this stack?
4 ft
12 ft
Each piece of wood is 18 inches long
The stack is 4 feet x 12 feet x 18
1.5inches
feet = 72 cubic feet
= 72 ft3 stack
A cord is 4 feet x 4 feet x 8 feet = 128 cubic feet (128 ft3).
So we will need 128 ft3 x 3
= 384 ft3 for the winter.
72 ft3
=
.1875
=
About 19%
384 ft3
or about one fifth (1/5th) of a year’s supply
Problems
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Trees per acre
Rafter length
Timber milling
Milling price
Acreage
Mortar Mix
Length
Window price
Arch
Roof
Stairs
Plumbing
Firewood