Are derivations important?May 7th, 2009 Are derivations, especially in Geometry, important? I’ve frequently posed this question to students over the years and have typically got the response − “No, if they are out of syllabus!” I disagree almost completely. Years back when I was in school, almost inadvertently, I got down to doing something really boring on a boring summer afternoon. I picked up Heron’s formula: Area = Where, s is the semi-perimeter of the triangle i.e. I admired its unwieldy look and got down to deriving it. Quite obviously, I first drew a triangle with the sides given.
I realized pretty soon that there wasn’t much headway I could have made without doing some construction. I did what any student would do. I dropped a perpendicular and did away with my first roadblock.
Then I wrote the known formula for the area of a triangle (something I should have done first!) Area of ΔABC Now I had two right triangles. Right triangles ! obviously Pythagoras theorem. Suddenly I had these equations. c2 = h2 + d2 … (1) b2 = h2 + (a − d)2 I knew that the answer had to be in terms of the lengths of the sides. I looked at the equations and did the most obvious operation to eliminate ‘h’ − I subtracted one equation from the other and the result was this − b2 − c2 = a2 − 2ad ⇒ 2ad = a2 + b2 − c2
I got the value of ‘d’ in terms of a, b and c. I knew I was getting somewhere. I substituted this value in the first equation to write ‘h’ in terms of a, b & c.
After this I did my last step and that was simply substituting the value of ‘h’ in the formula for area. This is what I got. Area of ΔABC Looked scary but it worked as well as Heron’s formula (which probably was a few steps away). Now if I had a,b and c, I could find the area of the triangle! What this did was it removed my mental block towards Heron’s formula, and that is important. In Geometry, you will almost always remember the formula/theorem but when faced with a question, you will not know which theorem to call for help when. And that is what derivations do. They give you the power over theorems, and thus Geometry. So next time if you get a theorem, attempt its derivation. You might not always be successful, but you would have made a good beginning in the direction of mastery over Geometry. - Pavan Entry Filed under: General, Student Zone
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21 Comments Add your own
1. AHILYA | May 8th, 2009 at 9:46 am
a very nice method.really its very nice and easy meyhod.
great brain
2. guntash | May 11th, 2009 at 2:32 am
even easier method
just use cosine rule
3. vaishnavi | June 11th, 2009 at 6:50 am
its just great.It really provides a positive outlook towards the so called “boring derivations”.
4. rachit | June 15th, 2009 at 6:18 am
give me knowledge about comercein 11 to my mail id
5. shubham | June 17th, 2009 at 9:30 pm
it is quite good from the boring hindi lectures.it gives shape to our mind.
6. shubham | June 17th, 2009 at 9:35 pm
give me some information about schools in bhopal on my phone#+919407001937
7. mubeen ahammed | July 1st, 2009 at 6:32 am
give me some information about schools in kerala on my email id
8. sarthak | July 18th, 2009 at 9:23 am
can u post some more easy methods for some other difficulties of geometry
pls mail it to my mail id
9. rabi | July 18th, 2009 at 9:20 pm
its good 2 kept question.all the student can watch this web like me.thank 4 this
10. merin | July 30th, 2009 at 6:00 am
yehh ,, Itz a very good site …Heron’s formula is easy ..But i think proof is not needed
11. Pradipti | August 2nd, 2009 at 6:22 am
derivations are really important great brain
12. Abhishek Sharma | August 4th, 2009 at 6:47 am
Sir, these innovative methods had made me so good in mathematics that I cannot score <100 (that too a linear inequality)
13. mukesh | August 8th, 2009 at 8:49 am
thanx sir but do you know any shubham sukhwal
14. Yogesh Kulkarni | August 19th, 2009 at 12:03 am
Pavan, You look very intilligent. I must appreciate your effort. If you have such formulas & intilligent excercises please mail me on kulkarniyogesh68@gmail.com. I am waiting for your reply. All the best for your career.
Yogesh kulkarni
15. vikash | August 20th, 2009 at 4:19 am
Vikash
It would not have not have been so scary if u would have solved further.But thought of a good way.
16. Vishal Vishwakarma | September 29th, 2009 at 8:14 pm
Merit nation is an excellent site where we can study with fun. In this we think that we are spreading our name on net but we are actually studying.
17. Vishal Vishwakarma | September 29th, 2009 at 8:16 pm
I was sad to discover a day that we could only vote 5thumbs up and down a day. I would like to request Merit Nation to increase it’s quantity.
18. naavya | October 13th, 2009 at 3:28 am
inter b.tek
19. shruthi | October 20th, 2009 at 7:54 am
nice one, that’s a great approach towards studies but the issue is larger when the going gets tough. give me a choice and i’ll take up knowledge any time! students need encouragement which comes so scarce in midst of all competitive exams, entrance exams and school exams.
20. jes | January 18th, 2010 at 9:17 am
superb
21. Business Directory | November 22nd, 2011 at 2:30 am
Markedly well executed post!!
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