Lesson GRADIANS
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This lesson provides an overview of gradians. It will be short because gradians are not used very much anymore. Degrees and radians are widely used instead. The main purpose of this lesson is to tell you what a gradian is so that you you can understand the difference between a gradian and a radian. Since the names are so similar, they might be easily confused with each other. Your calculator might allow you to enter and display numbers in gradians as well as radians and degrees. Press the wrong selection and you get a vastly different answer. If your calculator displays RAD, then you have radians. If your calculator displays GRAD, then you have gradians. The other names for gradians would be "gon" or "grade" or "centesimal degree". REFERENCES <a href = "http://en.wikipedia.org/wiki/Grad_%28angle%29" target = "_blank">http://en.wikipedia.org/wiki/Grad_%28angle%29</a> <a href = "http://everything2.com/title/gradian" target = "_blank">http://everything2.com/title/gradian</a> <a href = "http://gwydir.demon.co.uk/jo/units/angles.htm#gradian" target = "_blank">http://gwydir.demon.co.uk/jo/units/angles.htm#gradian</a> <a href = "http://www.eng-tips.com/viewthread.cfm?qid=128106&page=8" target = "_blank">http://www.eng-tips.com/viewthread.cfm?qid=128106&page=8</a> DEFINITION OF GRADIAN A gradian is another way of dividing a circle into smaller sections. It functions like a degree only it is slightly smaller. There are 400 gradians in a circle. There are 4 quadrants in a circle. Each quadrant has 100 gradians in it. This provides certain advantages over the degree system, but also provides certain disadvantages. The disadvantages outweighed the advantages because degrees and radians are widely used today whereas gradians have mostly gone out of use, except in certain areas like surveying. Some compasses also use gradients rather than degrees. The term "gradian" should not be confused with the term "gradient". They are not the same. COMPARISON OF GRADIANS AND DEGREES There are 400 gradians in a circle. There are 360 degrees in a circle. The ratio of degrees to gradians is 360/400 = .9 gradians = degrees / .9 Degrees = gradians * .9 Example: degrees = 400 * .9 = 360 gradians = 360 / .9 = 400 COMPARISON OF GRADIANS AND RADIANS There are 400 gradians in a circle. There are 6.283185307 radians in a circle. The ratio of radians to gradians is .015707963. This is more easily remembered as pi/200. pi is equal to {{{pi}}} is equal to 3.141592654. pi/200 = 3.141592654/200 = .015707963 Your scientific calculator should have a {{{pi}}} key that allows you to retrieve that constant very easily. gradians = radians * (200/pi) radians = gradians * (pi/200) Example: radians = 400 * (pi/200) = 6.283185307 gradians = 6.283185307 * (200/pi) = 400 COMPARISON OF RADIANS AND DEGREES There are 360 degrees in a circle. There are 6.283185307 radians in a circle. The ratio of radians to degrees is .017453293 This is more easily remembered as pi/180. pi is equal to {{{pi}}} is equal to 3.141592654. pi/180 = 3.141592654/180 = .017453293 Your scientific calculator should have a {{{pi}}} key that allows you to retrieve that constant very easily. degrees = radians * (180/pi) radians = degrees * (pi/180) Example: radians = 360 * (pi/180) = 6.283185307 degrees = 6.283185307 * (180/pi) = 360 Check the references for more detailed explanations and some interesting tidbits regarding gradians.
