10 Everyday Reasons Why Trigonometry is Important in your Life?

Mathematics is a subject that is vital for gaining a better perspective on events that occur in the natural world. A keen aptitude for math improves critical thinking and promotes problem-solving abilities. One specific area of mathematical and geometrical reasoning is trigonometry which studies the properties of triangles. Now it's true that triangles are one of the simplest geometrical figures, yet they have varied applications. The primary application of trigonometry is found in scientific studies where precise distances need to be measured.

The techniques in trigonometry are used for finding relevance in navigation particularly satellite systems and astronomy, naval and aviation industries, oceanography, land surveying, and in cartography (creation of maps). Now those are the scientific applications of the concepts in trigonometry, but most of the math we study would seem (on the surface) to have little real-life application. So is trigonometry really relevant in your day to day activities? You bet it is. Let's explore areas where this science finds use in our daily activities and how we can use this to resolve problems we might encounter. Although it is unlikely that one will ever need to directly apply a trigonometric function in solving a practical issue, the fundamental background of the science finds usage in an area which is passion for many - music! As you may be aware sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. And this means that sound engineers and technologists who research advances in computer music and even hi-tech music composers have to relate to the basic laws of trigonometry. 

Trigonometry finds a perfect partner in modern architecture. The beautifully curved surfaces in steel, stone and glass would be impossible if not for the immense potential of this science. So how does this work actually. In fact the flat panels and straight planes in the building are but at an angle to one another and the illusion is that of a curved surface. Neat huh!

Digital imaging is another real life application of this marvelous science. Computer generation of complex imagery is made possible by the use of geometrical patterns that define the precise location and color of each of the infinite points on the image to be created. The image is made detailed and accurate by a technique referred to as triangulation. The edges of the triangles that form the image make a wire frame of the object to be created and contribute to a realistic picture. Several imaging technologies that apply the concepts of trigonometry find usage in medicine. The next time you go in for an advanced scanning procedure, be sure to check out how the sine and cosine functions you learn at school find a practical application is medical techniques such as CAT and MRI scanning, in detecting tumors and even in laser treatments. Whoever said studying math has only an academic value! Need other reasons to know how formulae in trigonometry make life easier for you? Now we all use patterns and symmetry in relating to objects around us. For instance there is a need for harmony and symmetrical agreement even if you are just redecorating your home. You need to be sure about angles and positioning when deciding lighting arrangements. And although you won't need to write out sine formulae for this one, you will still be using the basic laws of triangles in deciding the best angle to show off that trendy lamp on your study table!

Trigonometry is an arty science that can be used to measure the heights of mountains? So why would we want to measure the heights of mountains. Because this information is of great value for aircraft designing and navigation. And if this sounds overly technical think about the time when you last took a vacation at a hill station. You might be surprised how much this information comes in handy to tourists, for example those with medical conditions that prevent them from traveling to very high altitudes. So the next time you want to go trekking you might want to know the actual altitude you might be traversing.

Learning math sure makes us smart and adept at solving tricky situations. From tacking brain-teasers and jigsaws to the more complex crises, the application of basic laws of math and geometry are many. Not only does math provide a strong basis for resolving everyday issues, it undoubtedly helps handle situations with a positive approach.

trignometery

Source:http://www.mathworksheetscenter.com/mathtips/trigonometry.html

A brief history of maths

This is my first education related post,since the time I have entered the education sector. The mathematical world would be 3 part post, where I will be talking and posting about the development and evolution of maths and in the last part of this series will talk about the math around us!!

History of numbers and the number system

The concept of numbers probably originated with the need to count how many things are there in a collection of things. Thus, methods like fingers, pebbles in containers, marks on clay tablets (present day tally marks), notches on sticks, and knots on cords were developed for  keeping records and counting of numbers.The knots,notches,marks either represented a single number or a group of numbers.

Ishango Bone & associated history

As the civilizations grew and bureaucracy rose, the system of trades & taxes evolved, size of numbers increased, which lead to the development of more and more complex numbers and number system.

More recently, during the past 2,000 years or so !!, various systems of writing have been used to represent numbers. The decimal system or the base 10 system which is also known as Hindu-Arabic number system was actually discovered in India. The decimal  is based on ten symbols (0, 1, 2, . . . 9) and rules for combining them in which position is crucial (for example, in 504, the 4 stands for 4 units, the 5 stands for five hundreds, and the zero stands for no additional tens). In expanded form:

504=5x10^2+0x10^1+4x10^1

The Roman number system, which is still used for some purposes (but rarely for calculation), is made up of a few letters of the alphabet and rules for combining them (for example, IV for four, X for ten, and XIV for fourteen. The roman system didn’t have any symbol for zero,besides that it was based on addition of numerals- which was a major drawback of this system hence didn’t find much application except in watch dials!

eg: if i had to write 34 i will be writing  XXXIV.=10+10+10+4 and I had to write a million it would take me about half a million digits to represent it!

There is one more system around which our whole world revolves. It is the binary system—the mathematical language of computers and almost all the electronic gadgets which we use. Binary language uses just two symbols, 0 and 1, which can be combined in exponential form to represent any number. Eg: 

5=101=1x2^2+0x2^0+1x2^0

6=110=1x2^2+1x2^1+0x2^0

Notice the decreasing power of 2 which is same as we observe in decimal system.

Similar to binary system there many other number systems like hexadecimal (base 16) & octadecimal( base 8) which are used to represent bits and bytes in the world of computers.  

Watch this interesting video which covers how the maths has evolved in the the ancient time.

Understanding Numbers: 

Whole numbers:

There are different kinds of numbers. The numbers that come from counting things are whole numbers, which are the numbers we mostly use in everyday life. A whole number by itself is an abstraction for how many things there are in a set but not for the things themselves.

If I say 1 million, it may mean 1million Rs/dollar/pounds, cars, population of city, virus population in a sample etc etc!. In most practical situations, we want to know what the objects are, as well as how many there are. Thus, the answer to most calculations is a magnitude and a label connected to it in other words a number connected to a label.

Let us take an example:

If you traveled 160 Km in 4 hours, your average speed was 40 Km per hour, not 40. In this instance, 160, 4, and 40 are numbers/magnitudes; Km, hours, and Km per hour are labels. It is the labels which give meaning to numbers.

Without the labels numbers don’t have any real significant application. This reminds me of my school days where a ½ mark or 1 mark was deducted whenever the units were missing from the final answer!

Similarly when we teach kids counting on fingers it is important to realize that it is the number of fingers we are counting and not just reciting numbers.

That marks the end of the first post. In the next part will talk about fractions,symbols, probability and data handling!

thought source:
http://www.scribd.com/doc/58790528/All-About-Science
http://www.project2061.org
http://darkwing.uoregon.edu/~moursund/Math/mathematics.htm