Category: complex math

Trigonometry and Calculus

Why do those two words bring fear to the minds of most people?

Have you ever had a trigonometry course or a calculus course? If you were a science or math major in college then you almost certainly have taken those courses! Did you like learning that type of math? Was it fun for you or does it evoke bad memories?

Hopefully if you’ve had those courses, they were fun for you. I was thinking about that as I was reading this article I found below.  It briefly describes the history of trigonometry and calculus. Hope you enjoy it!

 

Discovering Trigonometry
Trigonometry is a category of mathematics that studies triangles, as well as the spatial relationships between triangle sides and degree angles between these sides. Trigonometry is used to define trigonometric functions.

Trigonometric functions describe the relationships between the angles and sides and are also applied to cyclical phenomena, such as waves.

Trigonometry itself is very similar to geometry, but is slightly more complex. It utilizes functions such as sine, cosine and tangent to analyze areas of angles. These and other functions of trigonometry are used in a variety of career fields including but not limited to: acoustics, architecture, astronomy, biology, chemistry, civil engineering, computer graphics, metrology, medical imaging, music theory and several other fields.

Trigonometry is taught starting in middle and high school. It can be taught as a separate course, but is also taught as a preliminary course for calculus. Trigonometry develops student’s knowledge of both pure and applied mathematics. College level trigonometry is required for several different career majors to help students develop a further understanding of angles and spatial relationships.

Trigonometry was first developed in the 2nd century BC by the Greek mathematician Hipparchus. Hipparchus developed what is known as the first trigonometric table. He used trigonometry, and other mathematical functions, to develop lunar and solar theories. He also used trigonometry to study the motion and orbit of the sun and moon. Though trigonometry was developed by Hipparchus, the study of triangles can be traced all the way back to Egyptian mathematics and Babylonian mathematics.

The Egyptians and Babylonians used trigonometry to develop theorems on ratios of triangle sides. The Babylonian astronomers used early trigonometry to measure the angular distances on the celestial sphere. They used this to detail records of rising and setting stars, planet motions, and solar and lunar eclipses.

During the Hellenistic period, the Greeks took the early Egyptian and Babylonian trigonometry and developed the chord, which developed the use of arcs. A chord of a circle is the geometric line segment whose endpoints are on the circle’s circumference. The chord joins two points on any curve, but it is not limited to an ellipse. The chord that passes through the center point of the circle also functions as the circle’s diameter.

The trigonometry that is currently used today was developed by European mathematicians, Sir Isaac Newton and James Stirling in the 17th century. Newton and Stirling created the general formulas that are currently used to solve trigonometric functions.
By: Dennis McLynn
Article Directory: http://www.articledashboard.com

Dennis McLynn is the Vice President of Strategic Marketing & Business Development for High Points Learning. HighPoints Learning (HPL) is a leader in Web-based math education and instruction. HPL offers an online math tutoring program that helps raise participants’ math scores an average of 15 points in pre and post testing. HighPoints Learning services the 3-12 grade market. For more information visit: www.ehighpoints.com

So with all of this history under your belt, you’re ready to go hit the trig books right?  😉

Have a great day!

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Does Math really Exist?

Here’s an interesting idea – is math really real or a creation of our human brain?

Check out this video about math as we know it – the relevant part goes up to the six minute mark.

Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS
Math is invisible. Unlike physics, chemistry, and biology we can´t see it, smell it, or even directly observe it in the universe. And so that has made a lot …

So what do you think about this? Does math really exist?

Have a great day!

 

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Complex Math and Mental Math

Is mental math necessarily complex math? I don’t think so!

I found a short article which helps to teach students how to deal with complex and mental math (as well as easy math)!

Check it out:

Mental Maths Activities That Are Beneficial

Considered a complex subject, most students find it intimidating and for most of them, as they age, it becomes more complicated. Though this is the case, it is an important part of life as it equips them with the necessary skills to face real life.

Easy Answers
Mental maths should be introduced from kindergarten grades to students who have a lower capacity of understanding maths. This should be done with easy to answer questions. If it is in a class setting, then the students should be presented with simplified math equations and the first one to get the right answer should shout it out. As this progress, it will eventually reach a point where the entire class shouts out the right answer as a team. As they age and get more equations correctly, then more complex math should be introduced. In this instance, students can use time tables, basic algebra and division facts. For instance this could be something that Y plus four equals 10 and the students should answer what Y is.

Complex Math
A large percentage of maths used in day to day life is mental math tricks. For instance, someone working at a store should figure out what 60% of $20 is, a driver is supposed to figure out how many hours he will drive to cover a 230 mile trip among others. This proves that math is an important part of life and as such, it is ideal to ensure that students solve mental maths equation every day. However, when carrying this out, it is important to ensure that it is age appropriate. For seventh graders 60% of $ 230 is ideal while for fourth graders 10% of 100 is appropriate. Students should be given the time to read the equation and work it out before providing the answers.

Story Problems
This is another important mental maths activity to indulge in. It should be on situational stories and students should be encouraged to work them out mentally. Also known as multi-mental math they are the best. This is attributed to the fact that they require more thought for the answer to be processed as well as mimicking the manner in which maths is used in real life situations. However, it is important to outline the equation in a manner that is easy to understand. Though challenging, these simple mannerisms when employed in the right manner, help students develop an instinctive accuracy handling mental maths.

By: Borat Noviak

Article Directory: http://www.articledashboard.com

To learn much more about the mental math tricks, maths tips can be found at mentalmathtricks.com/.

So  has this changed your mind? Do you believe that these tricks and exercises can helpyour child to learn complex math?

Let me know?

Have a super Memorial Day Holiday.

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Square Roots and Negative Numbers

So who says math isn’t complex? And is learning math really a complex process?

The basic rule of multiplying 2 negative numbers yields a positive number makes it seem impossible to get a square root of a negative number, right?

Well here’s a funny video which will show you how to figure out the square root of a negative number.

Algebra 2 – Complex Numbers – part 1 of 3
Now… YAY MATH would like to introduce to you the imaginary number ” i ” ! Check out how we simplify expressions involving the square roots of negative numbers. YAY MATH! Visit www.yaymath.org Videos copyright (c) Yay Math

 

Very interesting, don’t you agree?

The concept is cool but remember, there is NO paper throwing or airplane flying at Mathnasium!  😉

Have a great day!

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