The basic parts of MATHEMATICS are as follows.

**The word MATHEMATICS comes from a Greek word, mathema, which means, “Things learned.”**

Do this simple exercise:

- Count the chairs in the room.
- Get how many chairs are there
- Note that you learned this fact by counting.

This means that counting provides you a systematic way of finding how many things there are. It is a tool for learning.

**In general, Mathematics consists of tools for learning. It helps one learn in a systematic manner. **

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**The word ARITHMETIC comes from [Greek, ARITHMOS number + TECHNE skill] **

Arithmetic helps find the answers to problems that involve numbers. Knowing the fundamentals of Arithmetic, problems with large numbers can easily be solved mentally.

For example: Find the sum of 297 and 562.

- Imagine two stacks of 297 and 562 pennies.
- Transfer 3 pennies from the 562-penny stack to 297-penny stack.
- You now have two stacks of 300 and 559 pennies.
- This can be added quickly as 859 pennies.

**ARITHMETIC, literally, means “skill with numbers.”**

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**The word ALGEBRA comes from [Arabic, AL- the + JABARA to bind together]**

ALGEBRA uses the relationships among quantities to determine what they are. Algebra is a natural extension of Arithmetic. Many word problems requiring arithmetic can be solved more easily with techniques learned in algebra.

For example: Find three consecutive numbers that add up to 30.

- Let’s say the middle number is
**N**, - Then the next number is “one more” or
**(N+1),** - And the previous number is “one less” or
**(N-1),** - So, we have
**(N-1), N,**and**(N+1)**as three consecutive numbers. - The sum of these three consecutive numbers is 30.
- Therefore,
**(N-1) + N + (N+1) = 30** - Or,
**3N = 30** - Or,
**N = 10;**Therefore,**N – 1 = 9;**and**N+ 1 = 11** - Therefore, the three consecutive numbers are
**9, 10**and**11,**and we learn that the middle number of three consecutive numbers is always one-third of their sum.

**Thus, ALGEBRA, determines the value of quantities from the relationshp that binds them.**

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**The word GEOMETRY comes from [Greek, GEO earth + METREIN to measure]**

GEOMETRY provides an understanding of the relationships among locations so one can determine distances, areas and volumes to construct and manipualate things in space. It is fascinating to learn the properties of space. Questions, such as, “How to accurately measure the vertical height of a mountain,” are easily solved through geometry. Here is how you can find the width of a river without crossing it.

- Locate a landmark, such as a tree, on the opposite bank.
- Place a pole right opposite the tree on this side of the bank.
- The separation between the pole and tree would denote the width of the river.
- Tie a rope to the pole and start walking parallel to the river on your side of the bank.
- Use a sextant to measure the angle between the pole and the tree from your location.
- Find the location where this angle is 45 degrees.
- Measure the length of the rope between this location and the pole.
- This length would be equal to the separation between the pole and the tree.
- Therefore, this length will give you the measure of the width of the river.

**Thus, GEOMETRY determines useful values from the relationships among locations in space.**

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## Comments

I think this can be a helpful way to present this information. I think keeping it short and pertinent as you have may be the best. But then the question can arise how or with what tool do I decide that the 45 deg angle I desire has become 45 degrees? That’s just a suggestion and maybe it’s not pertinent to your point.

Here is an instrument that you may use to measure angles.

http://en.wikipedia.org/wiki/Sextant

In this example, you keep on measuring the angle at various distances as you walk, until you find the location where the angle measures at 45 degrees.

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Oh yeah. i get it, and know how to do this. My point was to give mass to the post as you have now done..

I loved plane geometry as a boy. I loved to write the proofs.

I loved it too, especially the proof of the Pythagorean Theorem. See Proof # 1 here.

http://www.cut-the-knot.org/pythagoras/index.shtml

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