Ziniah Beasley Shenandoah Valley Academy THE MATH CONNECTION

Ziniah BeasleyZiniah BeasleyShenandoah Valley AcademyShenandoah Valley Academy

www.shenandoahvalleyacademy.org/www.shenandoahvalleyacademy.org/

THE MATH THE MATH THE MATH THE MATH CONNECTIONCONNECTION

©2005 Ziniah Beasley

WHY DO I NEED ALGEBRA?WHY DO I NEED ALGEBRA?


BECAUSE…BECAUSE…

YOU

How Does Algebra How Does Algebra Connect To …?Connect To …?

ARCHITECTURE MUSIC

NATURETECHNOLOGY

RELIGIONHISTORY

ART

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As we explore some of these As we explore some of these areas, ask the Following:areas, ask the Following:

WHERE can I use this? WHAT am I looking at? WHO is/are the intelligent

designer(s)? HOW is it connected to Algebra?


Algebra and ArtAlgebra and Art

Cycleslithograph (1938)

Reptileslithograph (1938)

Where ?!!


Intelligent Designer : Intelligent Designer :

Mauritus C. EscherMauritus C. Escher

1898-19721898-1972


Math Connection:Math Connection:

SymmetrySymmetry

Tessellations:Tessellations:

reflections ,translations, andreflections ,translations, androtationsrotations

Graphing linear equations in Graphing linear equations in 3-D variables of x, y , z axis3-D variables of x, y , z axis


Algebra and ArchitectureAlgebra and Architecture

The Parthenon448-432 BC

Where ?!!


Intelligent Designers:Intelligent Designers:

Greek Architects:Greek Architects:

Iktinos Iktinos

and and

KallikratesKallikrates


Gold Mean: Gold Mean: AB/CB=CB/AC AB/CB=CB/ACratio of 5:8 ratio of 5:8 The Parthenon used ratio of 4:9The Parthenon used ratio of 4:9

Pythagorean Theorem:Pythagorean Theorem:The sum of the areas of the squares in the legs of The sum of the areas of the squares in the legs of a right triangle is equal to the area of the square a right triangle is equal to the area of the square on the hypotenuse:on the hypotenuse: a2 + b2 = c2a2 + b2 = c2



Algebra and MusicAlgebra and Music

Musikalisches W&uumlrfelspiel(Mozart Musical Dice Game)

Where ?!!


Intelligent Designer:Intelligent Designer:Attributed to:Attributed to:

W.A. Mozart1757-1791


Math Connection :Math Connection :

Laws of Probability


Algebra and TechnologyAlgebra and Technology

Evolution of Space Flight

Where ?!!


Intelligent Designers:Intelligent Designers:


Math Connection: Math Connection:

Parametric equations Parametric equations and projectile motion:and projectile motion:

sin sin θθ cos cos θθ tan tan θθ x= vcosx= vcosθθt+ x0t+ x0y= vsiny= vsinθθt +y0t +y0

Matrices : [a][b]Matrices : [a][b]


Algebra and HistoryAlgebra and History

NOAH’S ARK AND THE FLOOD

Where ?!!


Intelligent Designer:Intelligent Designer:

And God said Unto Noah:

“Make Thee an ark of gopher wood; rooms shalt thou make in the ark, and shalt pitch it within and without pitch. And this is the fashion which thou shalt make it of:



The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits.”

Genesis 6: 14-15


Math Connection: Math Connection:

What are the dimensions in feet?What are the dimensions in feet?

If 1 cubit = “length of a forearm” If 1 cubit = “length of a forearm” = 18 inches= 18 inches

300 cubits long 300 cubits long =________ft=________ft50 cubits wide50 cubits wide =________ft=________ft30 cubits high30 cubits high =________ft=________ft

About 450

About 75About 45


Algebra and ReligionAlgebra and ReligionWhere ?!!

12

456

3

7


And God said on the:

1st Day: “ Let there be light.”

2nd Day: “Let there be a firmament..”

3rd Day: “…Let the dry land appear” and Seas. Let the earth bring forth grass, the herb yielding seed, and the fruit tree…”



Intelligent Designer:Intelligent Designer:And God said on the:

4th Day: “Let there be lights in the firmament of the heaven to divide the day from the night.” (God made two great lights; the greater light to rule the day, and the lesser light to rule the night)

5th Day: “Let the waters bring forth abundantly the moving creature that hath life and fowl that may fly above the earth…”


Intelligent Designer:Intelligent Designer:And God said on the:

6th Day: “Let the earth bring forth the living creature after his kind, cattle, and creeping thing, and beast of the earth after his kind.” Also, “Let us make man in our image, after our likeness...”

7th Day: God ended his work which he had made; and He rested.

Genesis 1:3,6,9-12,14,16,20,24,27; 2:2



Natural Numbers:Natural Numbers:1,2,3,4,..1,2,3,4,..

Positive Integers:Positive Integers:0,1,2,3,4,5…0,1,2,3,4,5…

Whole Numbers:Whole Numbers:1,2,3,4,5,6,7,8…1,2,3,4,5,6,7,8…

Natural Numbers:Natural Numbers:1,2,3,4,..1,2,3,4,..

Positive Integers:Positive Integers:0,1,2,3,4,5…0,1,2,3,4,5…

Whole Numbers:Whole Numbers:1,2,3,4,5,6,7,8…1,2,3,4,5,6,7,8…


Algebra and NatureAlgebra and NatureWhere ?!!

What do all of these have in common ?



They have Fibonacci numbers:They have Fibonacci numbers:by adding the last 2 numbers you get by adding the last 2 numbers you get

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …Sunflower:

89 & 55 spirals

8 & 5 spirals


……More Algebra and NatureMore Algebra and Nature


……More Math Connection:More Math Connection: The Rainbow can be defined by the Quadratic Functions:The Rainbow can be defined by the Quadratic Functions:

Called ParabolasCalled Parabolas

Y= ax2 + bx +c

Studying time, distance and space Studying time, distance and space uses the Scientific Notation : uses the Scientific Notation :

c x 10c x 10nn, provided 1 , provided 1 << c<10c<10

and Limits and Infinity:and Limits and Infinity: ∞∞



Let them praise the name of the Let them praise the name of the Lord. For He commanded, and they Lord. For He commanded, and they

were created. He had established were created. He had established them for ever and ever. (Psalm them for ever and ever. (Psalm

148:5,6)148:5,6)

God made design with order and patternGod made design with order and pattern



When I consider thy heavens, the When I consider thy heavens, the work of thy fingers, the moon and work of thy fingers, the moon and the stars, which thou has ordained...the stars, which thou has ordained...

Psalm 8:3Psalm 8:3

I do set my bow in the cloud, and it I do set my bow in the cloud, and it shall be for a token of a covenant shall be for a token of a covenant between me and the earth.between me and the earth.

Genesis 9: 13Genesis 9: 13


Algebra and YOUAlgebra and YOUWhere ?!!



I will praise thee: for I am fearfully and wonderfully made; marvelous are thy works …

Psalm 139:14



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SUMMARY:SUMMARY:

We have seen the connection of Algebra in some of the following areas:

Art Architecture MusicNature Technology History

Religion

And with each Algebra topic we will study,

we will explore its math connection to you and to our Creator.

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Ziniah Beasley Shenandoah Valley Academy THE MATH CONNECTION