How to understand geometry

Geometry is all about POINTS, LINES, AND SHAPES.

These are POINTS.

A POINT is a LOCATION IN SPACE. It is usually represented on paper as a DOT.

When you connect points, you create a LINE.

A line is how you get from Point A to Point B, or from point B to point C!

A "LINE" continues forever in both directions (Arrows on both ends). A "LINE SEGMENT" has two end points. A "RAY" has one endpoint and continues forever in the other direction.

And when you connect lines you get SHAPES!

Here are some common shapes!

And these are some things you can make using SHAPES!

There are also 3D shapes!

And here are some examples of things made using 3D shapes. FUN!

I love Geodesic Domes!

FUNNELS are used by scientists and for cars.

Look at all the GEOMETRIC SHAPES in this picture of a city.

And all of these things were made using certain GEOMETRIC FORMULAS!

Think of each formula as a TOOL you can use to make something COOL!

POINTS, LINES, and SHAPES (2D OR 3D), all have their own PROPERTIES.

Points can have a LOCATION. "Location" is a property of a point.

Lines can have a LENGTH/MAGNITUDE. The magnitude of a line tells you how LONG the line is.

Lines can also have an ANGLE. Angles tell you how the line TILTS.

Lines can also have a DIRECTION. North? South? East? West?

Shapes can have an AREA. The area of a shape tells you how much SPACE (2D space that is) the shape takes up.

Shapes have a PERIMETER/CIRCUMFERENCE also. The perimeter of a shape is the length of the borders of the shape. Imagine the circle were a race track. How many feet long is the track?

3D shapes can have a VOLUME and a SURFACE AREA. The volume of a 3D shape is how much 3D space it takes up. The surface Area is the area of the surface of the shape.

There are all types of formulas for lines!

And some really smart people have already found formulas for the most common shapes.

But how would you find the Area or Perimeter of these shapes?

Or the Volume and Surface Area of a shape like this?

Well, that is what CALCULUS is for!!!

End

TRIVIA: They say that the shortest distance between two points is a STRAIGHT LINE. But do you know what the shortest distance between two points on a curved suface is called?

Apps:

GEOMETRYIQ by CLEF SOFTWARE INC. is a neat game for testing your geometry skills.

Explore geometric shapes with GEOMETRY PAD by ZonMobile

Examples:

HOW MUCH CANDY IN THE CANDY JAR?

How many Skittles are in the jar?

Well the volume of a right cylinder can be found on step 26, and the radius of the base of the jar looks to be about 2.5 inches. Height is about 12 inches. So the volume is about 236 cubic inches.

So if each skittle were 1 inch by 1 inch by 1 inch, about 236 could fit in that container. But skittles are about closer to 1/2, So now we are at 472.

I would also calculate the volume if each skittle were 1/3 cubic inches and get 708.

So there are anywhere from 472 Skittles to 708 Skittles in the jar. If I had better measurements I could get closer.

And If I took the AVERAGE of 708 and 472 I would get 590.

Hopefully my calculations were correct. Haha. I tried to do this once and miscalculated, but it was pretty good for a mental math exercise. haha