Conic sections on a Polar Graph

many people wonder what the heck is a conic on a polar? This is putting the redular shapes ofarabola, elipse, and hyperbola on a polar plane. It is simple yet effect but there are a few points that must be figured out first.

These are simple equations that must be memorized in order to graph a conic. Now take these simple equations and lets figure out how to graph it. Alough you still need more information. What? Yah ypu need to know how a graph will look just based off of the equation. It will save time instead of plug and chugging multiple points that takes a ton of time. Now no one has that one their hands so here are a few simple rules. 

That is pretty much all there is. Here is a sample problem worked. Find the eccentricity of the equation and what shape it is?

That is it. Enjoy the fun of a graph. 

Math is fun.

Her is a link to a math game that can pass hours of time in minutes. Literally. 

http://www.playkidsgames.com/games/mathfact/mathFact.htm

Polar coordinates

A polar coordinate is complicating the regular graph of the x,y plane. Polar coordinates are now radiuses and angles. It helps to know some conversion factors between the x,y plane and the polar one. 

These conversion factors allow one to go from regularnt complex. Now what doesnthe graph look like?  It is just a bunch of circles and lines but one must know their unit circle to know how to use the graph. 

You count out the circles by your r. So if it is 2 in the r place count put 2 circles. After that you look at the theta to see the angle such as pi/4 and so one. 

That is all just plug and chug and graph. Yay fun. 

Fun facts of the day

• The numerical digits we use today such as 1, 2 and 3 are based on the Hindu-Arabic numeral system developed over 1000 years ago.

• Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

• The smallest ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

• 2 and 5 are the only prime numbers that end with a 2 or a 5.

• The golden ratio of approximately 1.618 between two quantities such as lengths often appears in nature (tree branching, uncurling ferns, pine cone arrangements etc) and has been used throughout history to create aesthetically pleasing designs and art works such as Leonardo da Vinci’s Mona Lisa.

• Fibonacci numbers are named after Italian mathematician Leonardo of Pisa (better known as Fibonacci) who introduced them to Western Europe after they had earlier been described by Indian mathematicians. They are related to the golden ratio and proceed in the following order: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, .... Can you see the pattern?

• The number Pi (the ratio of the circumference to the diameter of a circle) can’t be expressed as a fraction, making it an irrational number. It never repeats and never ends when written as a decimal.

• Here is Pi written to 100 decimal places:
  3.1415926535897932384626433832795028841971693993751
  058209749445923078164062862089986280348253421170679

• What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion.

• The name of the popular search engine ‘Google’ came from a misspelling of the word ‘googol’, which is a very large number (the number one followed by one hundred zeros to be exact).

• A ‘googolplex’ is the number 1 followed by a googol zeros, a number so ridiculously big that it can’t be written because there literally isn't enough room in the entire universe to fit it in!

• Check out some more big numbers.

• You might have heard the word ‘infinity’ before or seen its symbol that looks like the number 8 placed on its side. Infinity means a limitless quantity or something that goes on forever. While it’s not really a number like 1, 2 or 3, infinity is often used in math as part of equations and formulas.

• 111111111 x 111111111 = 12345678987654321

• 12 + 3 - 4 + 5 + 67 + 8 + 9 = 100

• 
  

Elipses

What is an elipse? It is the sum of all points whose distance from two distinct fixed points, foci, is constant. 

this video explains everything to know about an elipse

► 6:51► 6:51www.youtube.com/watch?v=pLXR0yHmUmg

Parabolas

What is a parabola? Well it is the set of points that have the same distance from the focus and directerix of one other point.

Key things to remeber when solving for Parabolas. 

1 Solve for the square

2 when solving rember to take the second term (bx) and divide the b by 2 then square

That is all.