why do we study geometry
The WHY of geometry depends on how you want to look at the world you live in.
If you are a pragmatist, geometry is a branch of practical knowledge which allows you learn more about the world around you, through surveying, measurements, and design, and then build more with accurate construction techniques.
If you are a philosopher, learning how to construct proofs will teach you how to think logically, and not make stupid decisions based on ignorance and faulty assumption.
If you are a student of history, then you know that the cultures with the smartest people, the best engineers, and superior technology, generally prevail over those without these assets. Geometry is part of the mathematics which underpins science and engineering.
And if you are just a plain student, who could care less about geometry or any other serious study other than the opposite sex, learning all that you can, while you can, may help you to prepare for a higher-income, satisfying job which will make you a more attractive partner for those you would want to date or marry.
Should none of these reasons satisfy you, then you need to study geometry because that is what you are required to do by whatever powers rule your life.
where do we find geometry
1. Area problems are one of the most common uses of geometry in our everyday lives. Let's say you need to install new carpet in your bedroom. How much carpet will you need to buy? Measure your room's length and width and then multiply them together to find out how many square feet of carpeting is needed. This is represented by the formula A = L x W, or area equals length times width. If, for example, your room is 12 feet by 10 feet, you will need 120 square feet of carpet.
2. Another area problem you may encounter is determining how many cans of paint to buy to cover your walls. The label on the gallon of paint tells you it will cover 400 square feet. You measure your walls and find that the room you want to paint has walls of the following dimensions: 10 ft x 10 ft, 10 ft x 8 ft, 10 ft x 10 ft and 10 ft x 8 ft. So you need to cover the areas of 100 square feet + 80 square feet + 100 square feet + 80 square feet = 360 square feet. Your room can be single coated by one can of paint.
3. Perhaps you are planning a garden. A bag of fertilizer says it can cover 100 square feet. You need to know how many bags you will need. Measure the area of your garden (length times width) to find your area. Let's say my garden measures 40 feet by 20 feet. That means I need to cover 800 square feet of area with fertilizer. Divide 800 by 100 and you get 8. We need 8 bags of fertilizer for my garden.
4. Let's say you want to fence in the garden we just mentioned. Find the perimeter to answer this question. Add up all four sides to get the perimeter - 40 +20 + 40 + 20 = 120 feet. You will need 120 feet of fencing to enclose your garden.
5. Volume involves three dimensional space. You could use volume to find out how much cement mix it will take to pour a walkway or how much sand is needed to fill a sandbox. Let's look at the sandbox example. You have built a sandbox that is 5 feet long by 5 feet wide. The sides are 6 inches tall. Volume is length times width times height or V = L x W x H. Six inches equals one half of a foot, or 0.5 feet. Our equation would be 5 x 5 x 0.5 = 12.5 cubic feet. It will take 12.5 cubic feet of sand to fill our sandbox. A fifty pound bag of sand is approximately half a cubic foot, so 25 bags would fill the sandbox completely full, or 12 and 1/2 bags would fill it half full, leaving room for sand toys and kids.
Uses of geometry in the workforce
6. Whenever you build something, you will encounter geometry. Professions such as carpentry and engineering make regular use of geometry problems.
7. Computer aided drafting and computer graphics for video games and movies use geometry extensively. The computers do a lot of the math for us now, but the calculations they use to do their work is deeply rooted in geometry.
8. Land surveying, navigation and astronomy all use geometry in their calculations.
9. Geometry is used in the medical field for imaging, modeling, and more.