triangles

Fraction

Fraction

DIVIDING TO EQUAL PARTS

DIVIDING TO EQUAL PARTS

WAY TO DIVIDING TO EQUAL PART AND SIMPLIFY

1. ONE THIRD OF AN INCHES
2. TEN PERCENT OF CUTTING WASTE

SECTION CUT and 360 degree rotation

SECTION CUT AND 360 DEGREE ROTATION

AREA TO VOLUME

AREA TO VOLUME

SECTION CUT

SECTION CUT

Under The Curve Area, Above The Curve Area and The Average Area

The under the curve, above the curve and average Areas

LENGTH TWO AND THREE DIMENSION

RECOGNIZING OF THE LENGTH

FORMULAS FOR THE UNKNOWN LENGTH OF TWO AND THREE DIMENSION

The box

the box

3d 

•  The starting point is (x =0, y =0 and z =0) called origin point. 
• ( x =1, y=1, z=1) = extending x  one unit in the positive direction, extending y one unit in the positive direction and extending z one unit in the positive direction from the original point. 

Circle

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CIRCLE BASIC

1.  Radius
2. Diameter
3. Circumference
4. A line passing through a circle * JUST TOUCH the surface * is called TANGENT LINE

SPHERE 

• Any line from the center of the sphere to the surface is equal called Radius

a cube is having six surfaces

A CUBE IS HAVING 6 SURFACES

oblique and surfaces

Practical problem for caculate the area of the room and the volume of the refrigerator

HOW to calculate the area of a room in our home?

1. unit for the measurement of the length is feet (foot is singular)
2. The area of the closet
3. The area of the room

THE VOLUME OF THE REFRIGERATOR

 (feet) X (feet) = feet^2

(feet) X (feet) * (feet) = feet^ 3

Area and volume

AREA AND VOLUME

To find the area of a square or the rectangle, we need to know the base length and the height

VOLUME

• the base
• the height
• the depth

The volume has six surfaces:

• the button
• the top
• the left side
• the right side
• the front 
• and the back

3D

THE 3 DIMENSION,

FROM B

• The x, y and z axis
• lines parallel to the x-axis 
• lines parallel to the y-axis
• lines parallel to the z-axis

FROM A

Connect the points, we have the 3D picture.
KEY WORDS:

1. DEPTH, in this picture, lines that parallel to the y-axis
2. HEIGHT, parallel to the z-axis
3. WIDTH, parallel to the x-axis

slope

SLOPE

It is the importance factor in the relationship of X and Y; the horizontal vs. the vertical line; raise vs. run... these pair terms are being called differently having the the same meaning.

SLOPE IN EVERYDAY LIFE

1.  roof
2. hill
3. uneven surface

Golden Rectangle

GOLDEN rectangle can be seen commonly as these shapes

• THE texbook
• the cellphone
• the television screen
• the monitor
• sheet of paper
• the room
• ???

area and volume

AREA: To find the area of the square or the rectangle, multiply X to Y

For example: Let X = 5 and Y = 5.  this is a square because the length of the X is equal to the Y's.

area = (5) * (5) = 25 -->this does not have the unit

BUT we say the X = 5 feet and the Y = 5 feet then

Area = (5 feet) * ( 5 feet) = 25 ft^2 (ft^2 = square feet)

WHAT ABOUT THE VOLUME? there is only one more dimension to include.

Let say: X = 5 Y = 5 Z =5

Volume of a cube = 5*5*5

two and three dimensional square and rectangle

THE BASIC IN DRAWING

• Point
• line
• vertical
• horizontal
• diagonal
• parallel lines
• right angle

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The two dimension picture has only the X and Y but the three dimensional picture is having X, Y and Z.  The question is how do we draw the three dimensional object into two dimensional paper? OBLIQUE!

FROM THE PICTURE

1. The vertical line is Z
2. the horizontal lines are X and Y
3. Three lines intersect each other as drawing on the left called the original point. 

COMPARISON

• The square is having parallel lines as two dimensions or three dimension.  The look is a bit different. 
• Key words: the point to point connection, parallel lines, and intersection with right angles. 

Signs

WHEN WE LOOK AT THE 2D

1. Let name the horizontal line as X
2. Let name the vertical line as Y
3. As X intersect Y, it is the origin point

FOR REFERENCE 

1. Moving right from the origin point is the positive sign
2. Moving to the left from the origin point is the negative sign
3. For the Y, moving up from the origin is positive
4. Moving down from the origin is the negative

We can name X as something else and Y as something else.  For example;  we can say the X as the supply line and the Y as Demand.   

WordMeaning

A point is a dot on the paper.

A Line is connecting with two points or dots

 Closed loop of  three points forming an area

It is good idea to learn these words because it is the key concept for drawing in three dimension.  

welcome

Thank you for visiting my pages.  This site is about the art and the math relating to it.  The drawing, the math, and the 3d world, and 2d papers will be written as days to come.

Everything we see in the real world, it is three dimension.  But how do we take that image and put it on the papers so that we can calculate the volume, area or write the name of it?