### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

You can change this under Settings & Account at any time.

# math

No description
by

## Nisy Nisy

on 30 January 2013

Report abuse

#### Transcript of math

The Journey of Big O Who is the largest here? It's me! No!! I'm larger than you! I'm the largest! Why? With the same perimeter ... 2 2 = Lx - x 2 Area (A) = x ( L - x ) 2 L Let’s start with rectangular How can we know that
A is max or min? 4 x = L max min A or A when 4 x = L Finding maximum of A 2 dx d (A) 2 L - 2x dx 2 d (Lx - x ) = 0 = 0 ( ) L 4 When x = L x = L x = L 2 4 6 A = 0 A = L 2 2 16 A = L 18 MAX lower lower so A will be the maximum when x = L 4 L n h ¶ n ¶ - ¶ 2 n Perimeter of Jen = L Equilateral polygon, with n sides, consist of n isosceles triangles angle around the point (center) = 360 or 2¶ 2¶ n Note! Equilateral polygon is a polygon which has all sides of the same length ... Note! To find area of Jen, we need to find area of a isosceles triangle Let's call her "Jen" Hi, I'm Jen To find area of a isosceles triangle, we need to know the height of the triangle To know the height of the triangle, we have to encounter Trigonometry!!!! tan ¶ - ¶ = h 2 n L 2n h = L tan ¶ - ¶ 2n 2 n Area of a triangle = 1 . base . height 2 = 1 . L . L tan ¶ - ¶ ( ) ( ) ( ) 2 n 2n 2 = L tan ¶ - ¶ 4n 2 n 2 2 ( ) 0 = So Jen is composed of n isosceles triangles Area of Jen = n . area of a isosceles triangle Area of a triangle = 1 . base . height 2 !@#\$%%@!@##%\$%^\$#@& But don't worry, it's just basic x Opposite Hypotenuse Adjacent sin x = cos x = tan x = O H A H O A n area of a triangle = L tan ¶ - ¶ 4n 2 2 2 n ( ) And let ¶ = y or n = ¶ n y L y tan ¶ - y 4¶ 2 ( ) 2 L y sin x cos x = 4¶ cos ¶ - y sin ¶ - y 2 2 2 sin A = cos (90-A)
cos A = sin (90-A)
tan A = cot (90-A) sin y cos y Jen's area cos y sin y y 4¶ 2 L L y cos y 4¶ sin y 2 = We want to proof that circle has the largest area so let n ∞ If
Jen
has 5 corners Pentagon 10 corners Decagon 18 corners Octdecagon ∞ corners or x 0 ( from letting ¶ = x ) n L 4¶ cos y sin y y lim 2 y 0 1 1 = L 4¶ 2 L (Perimeter of a circle) = 2¶r Perimeter of a rectangle = L 4¶ r 2 2 4¶ = Note! = So complicated!! n = ∞ ¶r 2 Let us explan about this. Next, take look at equilateral polygon that has n sides (or n corners) 2 2 L - L - x = L - x x To take this journey, you must know
basic calculus
basic trigonometry
basic geometry The Journey of Big O L 2n cos 0 = 1 0 0 0 0 lim sinA A A 0 = 1 Note! so area of Jen is n . L tan ¶ - ¶ 4n 2 n 2 2 ( ) n = 5 n = 10 n = 18 Circle Area of a Circle Who has the largest area?
and You are WINNER, Big O !!
Full transcript