MATHEMATICAL LANDSCAPING

Loreen JordanMS 110 W1

Professor Shari Lewis

Welcome !

• Mathematics as I have come to find out is even in gardening!– From the lay out of your planting area– Plant placement– Sprinkler system layout• Wow so much math • so little time!

Your assignment if you choose to accept it….

•Design a garden • dimensions of this garden are: 106

feet x 43 feet x 33 feet x 108 feet

•Place plantings • you will have pictures and maturity

dimensions' of plants

•Placement of sprinkler system• where will the heads go and what

type will you use.

***You can choose either to do just the planting arrangements or the sprinkler layout (due to time)***

Figuring the area of your Garden

This is an easy step you will need to determine the area in square feet to assist in drawing your gardenArea = Length x width Area in square feet = Length x width x 12

43'

108'

106' 33'

Existing trees

Existing trees

Existing trees

Existing trees

Existing trees

Existing trees

The dimensions of the area are 43 x 106 x 108 x 33

Plants you have to choose from HOSTAS

Eye declare18” diameter x 18” height

full/part shade

Golden Tea Cup 9” diameter x 11” height

Full/part shade

Heavenly Tiara 18” dia. X 14” height

Part Shade

Hacksaw

22” dia. X 11” height

Full/part shade

Hadspen Blue22” dia. X 18” height

Part Shade

The Razor’s Edge

11” dia. x 9” height

Full/part shade

Plants you have to choose fromFerns

Japanese Painted Fern12” dia. X 24” height

Full Shade

Japanese Shield 24” dia. X 24” height

Full Shade

Lady Fern30” dia. X 30” height

Sun/part/full shade

Christmas fern24” dia. X 12” height

part/full shade*** remember that the size is the diameter of the mature plant

Now how to figure out how many plants you will need

You have the diameter of each plant. You will need to figure out how many plants it will take to fill the area while not allowing the plants to touch. And make it look good.

You will need to determine the area of your circles and how many you will need. To figure the area of a circle : A = pi R(squared)

Sprinkler layout

Laying out the sprinkler system You will need to lay your lines , determine the type of heads to use and where to place them for best coverage. If you were to do this project for real you would also need to determine the amount of time each head would need to run for, but here we will not be doing that. It involves type of soil, how much sun, slope of grade….

Sprinkler layout•Much like determining the amount of plants needed you will need to determine how many sprinkler heads and what type.

•You will have four different degrees to work with 45, 90, 180 , and 360.

•You will have two types to choose from • the first is a spray head

which sprays a distance of 5 feet

• the second is a rotary head which sprays approximately 10 to 20 feet.

•You will need to remember that overspray is bad (overspray is when the water from one head overlaps the water from another causing an area to receive twice as much water. )

Now for the Math Stuff

When determining the area of a circle you will need to know either the radius or the diameter. Lets say your plant is 24” in diameter what is the total area of this plant? The diameter is twice as much as the radius. 24/2= 12 Your radiusArea = radius squared times pi. So the area of your plant will be 12 squared x 3.141 so the total area of your plant is 452.304

24”diameter

12” radius

The area is 452.304

More Math to figure outTo lay out a sprinkler system and your head is a 45 degrees you will need to figure the area of the sector. To do this you will need to create a fraction that has: the degrees from the sector’s central angle as the numerator, and 360 degrees as the denominator. Take the fractions down to lowest terms. Figure out the radius of the circle. Find the area of the circle. Divide the area by 360, then multiply by the number degrees in the partial circle. (www.wikihom.com)

Sector 45 degrees

Diameter is 12 cm

Area of sector = 45/360(6) squared x pi = 1/8 (36) x pi = 36/8 pi = 36 x 3.1415/8 = 14.136

You may use this grid to design your garden…. Have fun!

Helpful websites to use

www.wikihow.comwww.mathopenref.comwww.worsleyschool.netwww.mathsisfun.com