Using Math to Build My House

Jeff Goodmangoodmanjm@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

8 ft

80”

96”

802 + 962 = (rafter length)2

125”

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 inchOn each cut?

2”

He’ll make another cut that is 1” thick, leaving 8” behind.

How thick should the whole piece be?

8 + 2 + 1 + (2 x 1/8) = 11 ¼

1”

Remember, each cut removes 1/8” of wood.

$170 x 5 =

We have almost this many 1000 board feet of 1” boards.

$850

Let’s estimate to see if he did this right.

225

90

50

250

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).

Mortar Mix 1:3

cement sand

I have 18 bags of cement.

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?

How wide is one board?

33 1/16 + 3 ½ = 36 9/16

1 ¾

$597.65 x .7 = $418.36$597.65 x .7 = ?

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

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

RISERS

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:

8 feet96 inches / 10 = 9.6 inches per stair

= a little more than 9 19/32

TREADS

How did I do with the formula for comfort?

2 x (riser height) + (tread length) = between 24 and 26 inches

Risers = 7.9 inchesTreads = 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

2” x 1 ½” x 2” T

What is the naming convention for T’s and Y’s?

A waste pipe should be sloped 1% - 2%. How much should it slope per foot?

x

12=.01

x =.12

I know that 1/8” is .125”, so a 1% slope is a little bit less than 1/8 inch per foot.

We burn about 3 cords of wood a year to heat our house.cords

A cord is a 4’ x 4’ x 8’ stack

Approximately what fraction of our yearly supply of wood is this stack?

12 ft

4 ft

Each piece of wood is 18 inches long

Remember, we need 3 cords (each 4’x4’x8’) for the winter.

A cord is 4 feet x 4 feet x 8 feet

The stack is 4 feet x 12 feet x 18 inches

72 ft3

384 ft3

= .1875 = About 19%

= 72 cubic feet1.5 feet

= 128 cubic feet (128 ft3).

So we will need 128 ft3 x 3 = 384 ft3 for the winter.

or about one fifth (1/5th) of a year’s supply

= 72 ft3 stack

Problems• Trees per acre• Rafter length• Timber milling• Milling price• Acreage• Mortar Mix• Length• Window price• Arch• Roof• Stairs• Plumbing• Firewood