|
|
Algebra and Geometry Facts - Shortcuts
|
Views : 663
|
|
Tagged in : Shortcuts
|
|
|
Report This Scrap as Inappropriate
We request you to choose the appropriate categroy and subcategory that suits your
objectionable concern about the scrap, So that our team can review and find out whether it violates our Guidelines or the
scrap is not suitable for all viewers.
|
Interesting and Little-Known Algebra and Geometry Facts
Here are a few helpful and neat little facts that evade most students and teachers of algebra and geometry:
a) Though everyone can factor a^2 - b^2, a^3 - b^3, a^3 + b^3 and a^4 - b^4, most folks do not know that:
a^4 + b^4 = (a^2 + ab(sqrt(2)) + b^2) (a^2 - ab(sqrt(2)) + b^2
b) An approximation exists for the factorial function (for large n) which seems hardly related but works:
Stirling's Formula ---> n! ~~ e^(-n) n^n sqrt(2 (pi) n)
c) The area of any regular polygon of n sides, each of length x, is given by:
Area = (1/4)nx^2 (cot(180°/n))
d) The radii of circumscribed (R) and inscribed (r) circles within such regular polygons are given by:
R = (x/2) csc (180°/n) and r = (x/2) cot (180°/n)
e) The radius of a circle inscribed within any triangle of sides a, b, and c with semi-perimeter s is given by:
r = (sqrt (s (s-a) (s-b) (s-c)) / s
e) The radius of a circle circumscribed about any triangle of sides a, b, and c with semi-perimeter s is given by:
R = abc / 4 (sqrt (s (s-a) (s-b) (s-c))
f) The perimeter P and area A of polygons (of n sides) inscribed in a circle of radius r is given by:
P = 2nr sin(pi/n) and A = (1/2) nr^2 sin (2pi/n)
g) The perimeter P and area A of polygons (of n sides) circumscribed about a circle of radius r is given by:
P = 2nr tan (pi/n) and A = nr^2 tan (pi/n)
h) Factoring the seemingly prime expression a^4 + 4b^4 becomes (and there are a family of these)
a^4 + 4b^4 = (a^2 + 2b^2)^2 - (2ab)^2 (thanks to N. Hobson) |
|
By - Geethalakshmi, On - 2010-01-04 |
|
|
|
