2. QUIZTIME
- What does contradiction mean?
- What does consistency mean?
- Is it a contradiction or consistent?
1. I really don’t ever like sweet treats, but I do
like skittles!
2. Every person who eats skittles is really
awesome.
Momo eats skittles everyday.
So, Momo is awesome.
3. LOGIC
- Is it a contradiction or consistent?
1. All cats like treats and my cat does not
like treats
2. All scientists like math.
Sydney and Sid are scientist.
So, Sydney and Sid like math.
4. LOGICANDMATH
- Let’s look at a consistent statement in math:
- All numbers can be added together.
3 & 6 are numbers.
So, 3 & 6 can be added together.
5. EUCLIDOFALEXANDRIAFATHER OF GEOMETRY
- ELEMENTS IS ONE OF THE MOST INFLUENTIAL WORKS IN
THE HISTORY OF MATHEMATICS
- SERVING AS A TEXTBOOK FOR TEACHING MATHEMATICS UNTIL THE
LATE 19TH OR EARLY 20TH CENTURY.
- USED A FEW SIMPLE AXIOMS
- AXIOMS ARE THINGS THAT ARE TRUE. SINCE THESE THINGS ARE TRUE
IT MAKES OTHER THINGS TRUE TOO!
- WHAT ARE SOME EXAMPLES OF AXIOMS?
6. - Geometry is a kind
of mathematics that deals with
shapes and figures.
- Geometry explains how to
build or draw shapes, measure
them, and compare them.
- People use geometry in many
kinds of work, from building
houses and bridges to
planning space travel.
GEOMETRY
DEFINITIONS OF
7. - Euclidean geometry - The relationships between lengths, areas, and volumes of
physical objects
- Analytic geometry - Connects algebra with geometry
- Projective geometry - What is the shape of a shadow?
- Differential geometry - Connects calculus to geometry
- Topology - What happens when our shapes are made of play-doh?
MAJORBRANCHESOFGEOMETRY
8. BEFOREWETALKGEOMETRY
- Do you know what dimensions mean?
- What is an example of 1-Dimensional object?
- What is an example of 2-Dimensional object?
- What is an example of 3-Dimensional object?
9. - So, an 1-Dimensional object is a line.
- A 2-dimensional object is a square.
- A 3-Dimensional object is a cube or box!
DIMENSIONS
1-D
2-D 3-D
10. - What are length, area and volume?
- These are measuring something!
- Depending on how many dimensions you have will depend on which one you are
allowed to use.
- Let’s start with length.
LENGTH,AREA,ANDVOLUME
12. LENGTH
- Length measures 1-D objects.
- This is a line. Say hello!
- We want to know how long the line is.
- How do we figure out how long the line is?
- Well, we measure the length!
- If each tick is 1 inch, how long is the line?
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13. LENGTH
- What if we try to just measure the length of a square?
- What other things are we missing?
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15. - 2-D objects have two important measurements
1. Perimeter - adding the lengths of all the sides of a square together
2. Area - how much space is in a square
2-DOBJECTS
AreaPerimeter
16. PERIMETER
- Let’s say we wanted to walk around a square building, but we only wanted to measure one side of the building.
- We have two steps:
1. Measure one side of the building
2. Multiply that number by 4!
- For example,
- We measure one side to be 12 inches (that’s a very tiny building!)
- Perimeter = 4x12 = 48
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17. AREA
- If we a trying to figure out how much space (AREA) is inside our square
- There is a just a few steps…
1. If it is a square, measure one side of the square.
2. Multiply that number with itself
- In our case, one side is 9 inches long.
- So,
Area = 9x9=81
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18. AREA
- What is I wanted to measure how much space was in a cube or box.
- Can I use area?
- Let’s see.
- I measure one side to be 8 inches.
- Area=8x8=64
- But, that only tells you how much space is in ONE SIDE of the box.
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20. VOLUME
- Think about volume like this:
- If I poured water into a plastic
box,
- How much water would it take
to fill the box?
21. VOLUME
- To find how much volume is in a cube or box:
1. Measure one side of the cube
2. Multiply the number the number 3 times.
- For example,
One side is 10 inches long
- Volume = 10x10x10=1,000
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29. - There are two super duper
important things about circles
1. Circumference
2. Area
- Circumference is like the
perimeter of a circle
- Area is how much space is in
the circle!
CIRCLES
ROUND AND ROUND WE GO
30. - Circumference is if you wrap a string around a cup, how long is the string?
- Diameter is measuring the length of the string from one side of the circle to the other
side.
- Radius is half of the diameter
CIRCUMFERENCEANDDIAMETER
Circumference
Diameter
Radius
36. - Many artist have used geometry to make art work.
- Some of this art work using really complicated math equations to make moving art.
- Fractals are repeating patterns of geometry shapes that go on forever and forever!
- Let’s look at some. https://www.youtube.com/watch?v=FFftmWSzgmk
- At 12:48 in the video.
GEOMETRYANDART
