Introduction to Geometry

What is Geometry?

• The branch of mathematics that deals

with points, lines, angles, shapes, and

space.

• The study of sizes, shapes, positions,

and dimensions of things.

• The branch of math used to determine

lengths, areas, and volumes of objects.

• Plane or flat Geometry is about flat

shapes like lines, squares, circles, and

triangles.

• Solid Geometry is about 3 dimensional

shapes like spheres and cubes.

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Mandala Math Activity

Introduction to Geometry

How is Geometry used in everyday life?

1. Design, construction, and decorating a home or any building. The

geometric formulas for area and perimeter are often used for projects that

require room and object measurements. The measurements for the area

and perimeter of a floor are necessary for carpet and tile installation both in

rectangular and irregularly shaped rooms. They also assist interior

designers with creating floor plans and choosing the correct size of

furniture, tables, and rugs.

2. Outdoor projects make use of geometry as well. A gardener may calculate

the number of cubic feet (volume) of soil needed to fill a raised flower bed.

In this case, the correct equation would be base x height x width. The

formula for finding a perimeter may be used to determine how much wood

to purchase for building a fence around a yard.

3. Geometric formulas are also helpful for constructing craft projects,

informational posters, and frames for artwork.

4. Another example is computer imaging which uses geometric concepts and

figures to create animations and video games.

5. Geometry is critical in mapping. Mapping is an essential element in

professions such as surveying, navigation, and astronomy. From sketching

to calculating distances, they use geometry to accomplish their job.

6. In addition, professions such as medicine benefit from geometric imaging.

Technologies such as CT scans and MRIs are used both for diagnosis and

surgical aids. Such methods enable doctors to do their job better, safer, and

simpler.

What careers might you consider if you like and are good at

geometry?

• Architects (Buildings and Landscape)

• Engineers

• Carpenters

• Construction Workers

• Picture Framers

• Gardeners

• Astronomers

• Surveyors

• Navigation

• Artist• Medical Technicians

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Mandala Math Activity

A Mandala is a geometric design used in various

cultures as a representation of the universe. It

symbolizes perfection, harmony, and unity. They are

colorful and symmetric. Today, you will create your

own mandala using concepts of symmetry and

geometry! Both are important in math and art.

• Symmetry means that two or more

parts are identical on the opposite

sides of a plane, line, or point after a

flip, turn, or reflection.

• Reflection is a transformation in

which a figure is reflected across a

line, creating a mirror image.

• Angles are the figure formed by two

rays.

Supplies:

• Regular pencils; either with sharpeners or

lead refills

• Compasses

• Erasers

• Colored pencils, markers, and crayons

• 8.5” x 11” paper

• Scissors

Geometry is a type of math that deals with lines, shapes, and space.

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Mandala Math Activity

Instructions:

1. Using a compass, draw an 8-inch diameter circle.

a. Set the compass to 4 inches.

b. Place the point of the compass in the center

of an 8.5x11 paper in a portrait orientation so

the 8-inch circle can be drawn without

running off the page.

2. Using the scissors cut out the 8-inch circle as

carefully and as closely along the line as possible.

That helps make sure that the folding is

proportional.

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4. Once the circle is cut out, carefully fold it in half and then make a firm

crease along the fold. Fold the half circle in half again, and then once

more.

• In total, you are going to fold the circle in half 3x until it looks like a pizza

slice. Remember to firmly crease each side, but try not to rip the paper.

• It can help to use one side of the scissor handles to press down on the

paper firmly, especially when you reach the 2nd and 3rd fold. Be mindful

of the sharp side!

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Instructions (continued):

5. Once you have creased all the sides of your “pizza slice”, unfold it. You

should have a circle divided into 8 pieces, which you can easily see from

the lines, which should crisscross evenly.

6. Draw your name in bubble letters of whatever style you would like in only

one of the eight pizza pieces.

7. Once you are done writing your name, make sure the pencil outline of the

letters is bold and dark. If it is not, go back over the outline with the pencil.

8. Fold the circle in half so that your name outline is facing the inside. You

should be able to see which “pizza slice” you wrote your name on, thinly,

through the paper.

9. Shade in the other side of circle with the pencil until it is completely filled

in.

• Start towards the center with the first

letter of your name, then work your

way to the outer edge of the circular

cut out.

• Important!! The letters should touch

the TOP crease and BOTTOM

crease of the “pizza slice” section

and should be connected to one

another/touching each other

somehow.

• If you have a long name, you might

want to abbreviate.

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Instructions (continued):

10. When you carefully open up the circle, the outline of your name should be

reflected, lightly, in the “pizza slice” on the opposite half. Go over the

letters with the pencil, making sure they are bold and dark.

11. Repeat the process of folding and shading in the back of the circle, one

“pizza slice” at a time until the entire circle has been completed.

• Remember, whatever way you fold the circle in half and shade in a

triangle it will print the outline of your name on the opposite side (this is

also called a mirror image).

• Always go back over the lines to make sure they are dark and bold.

• Always fold your circle with the outlines of your names on the inside

and the shading on the outside, like a taco.

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Instructions (continued):

12. After the entire circle has been completed, the tops of the letters in one

“pizza slice” should meet up with the bottom of the same letter in another

section and form a complete circle.

15. Once you have completed this for all the rings of letters, fill each ring in

with a different color, color in the empty spaces, and watch your mandala

come to life!

This picture shows the

first letter M for the

Maddie example.

13. Carefully erase the lines connecting the top and

bottoms of your first initial in the different pizza

slices. The lines you erase should only be on

the borders of the pizza slices, and should only

connect the top and bottoms of the SAME

LETTER. Repeat for all the letters.

14. Once the lines have been erased, the letters

should merge to form some sort of ring. If you

desire, you can (carefully!) outline it in

permanent marker and erase the pencil. Or you can leave the pencil as is.