Cool Math Thread

[Iconoclast]

I prefer to use the y-intercept. You see, there are two processes of writing a squareroot in simplified radical form. I like the extended way:

√96 = √2 * √48 = √2 * √2 * √24 = √2 * √2 * √2 * √12 = √2 * √2 * √2 * √2 * √6 = √2 * √2 * √2 * √2 * √2 * √3

√2 * √2 * √2 * √2 * √2 * √3

1. Combine radicals that appear twice in a row by replacing both of them with a single number, the number under the radical.

√2 * √2 * √2 * √2 * √2 * √3 = 2 * 2 * √6

2. Combine any additional whole numbers.

2 * 2 * √6 = 4 * √6

3. Write your answer in simplified radical form.

4 * √6 = 4√6

And that...is the squareroot...of 96.

[Kit]

Is these some ultra adavanced tech? :D

Surds. It's using simple multiplication, except with square roots.

√2 multiplied by √2 = √4

And, because of the rules of factors, you can do these multiplications in different ways.

√12 = √6 * √2 = √4 * √3

[Iconoclast]

Stop stereotyping me for a nerd, people, if you all even have the definition of that word right. I mean, a geek, MAYBE, but there ain't nothing wrong with being made for math and computers worth being considered a nerd.

Geometry is fun! The theoroms and postulates are different...I didn't have fun memorizing those, either. But we learn how to find the value for a variable (x) by using the knowledge of multiple angles being either complementary (add up to 90 degrees), supplementary (add up to 180 degrees), vertical (equal to the angle opposite of it), or a linear pair (damn, I actually forgot that one...oh, well).

My favorite part about Geometry is learning how to find the perimeter, area, circumference, and volume of various shapes. Perimeter is pretty easy, right? The formulae for the perimeter of 2-D shapes should be quite obvious:

Square: P = 4s
Rectangle: P = 2l + 2w
Triangle: P = a + b + c

And then there's area:

Square: A = s^2
Rectangle: A = lw
Parallelogram: A = bh
Triangle: A = 0.5bh
Circle: A = (pi)r^2
Oval: ((r1 * r2) / 2) * (pi)
Trapezoid: It's been a long time....

The volume should be mostly obvious if you know how to find the base area of a shape, except for some shapes like pyramids and spheres, which I won't be covering in this post.

But what about finding the area of this shape?

http://i78.photobucket.com/albums/j112/rswedlo/ComplexShape.gif

Actually not that hard. Just pretend it was a rectangle, without that missing chunk, and multiply 36 * 30. I realize just now that there is an error I made with the dimensions of that shape...but just ignore that (12 + 12 + 8 /=/ 30). Then, just find the area of the missing chunk and subtract it from the entire shape.

I also liked the quadrilater specification rules we learned in Eighth Grade, but that's another story....

And, yes, pizzaman, algebra is equally, if not even more, should you somehow manage to apply it to real life, as fun. Simplified radical form squareroots are my faveorite. We had to learn things like, what's the squareroot of ten plus the squareroot of one hundred and twenty-five? And believe me, that has a nice answer.

My other favorite part of algebra is graphing lines.

Graph linear lines with: y = mx + b
Graph exponential growth/decay by using tables. (There are no tricks or universal equations that will help.)
Graph quadratic lines with (y =) ax^2 + bx + c (= 0).

Distance forumula: y = (sqrt.)(x2 - x1)^2 + (y2 - y1)^2(/sqrt.)
Midpoint formula: (x1 + x2) / 2, (y1 + y2) / 2
Quadratic formula (This son of a ***** took five pages of math to do some serious **** just to find the answer to some complex geometry-algebra cross math.):

y = (-b +/- (sqrt.)b^2 - 4ac(/sqrt.)) / 2a

I was a very neat scholar at the subject, and I'm still learning some interesting **** and memorizing long formulae.

[Iconoclast]

And....when did you take Geometry, Iconoclast? I have it now. It seems easy enough.Obviously, this year, since you just said you're taking it.

Over here, two years of math, social studies, three years of science, and four years of English are required for graduation (with several other specifications). But I'm taking four years of math (if I can cram Calculus in), and all the computer semesters I have room for, and possibly a Home Ec Independent Living class.

My favorite subjects, in order:

Computers (What can I say? I'm made for them, and I even have an understanding of binary by now, so who knows what I'll learn in the future?)
Math (almost as fun as a game of chess, but it's still a puzzle...fun writing all that confusing stuff I don't know that I actually understand)
Science (Stop stereotyping me as a nerd! What? It's interesting stuff! Especially the electromagnetic spectrum, specifically the advanced study of color.)
English (I really dislike the in-front-of-class presentations and large projects and such, but I really like the virtuous and comprehensive study of morality in life, and the Greek Mythology ain't too bad....
Social Studies (The least of my interests, but I'm looking for the life skills such as communication that it teaches in World and U.S. History.)I would like to post my schedule, but I think we've spammed this thread enough...yeah.... ... .. .

[pizzaman]

Geometry is fun! The theoroms and postulates are different...I didn't have fun memorizing those, either. But we learn how to find the value for a variable (x) by using the knowledge of multiple angles being either complementary (add up to 90 degrees), supplementary (add up to 180 degrees), vertical (equal to the angle opposite of it), or a linear pair (damn, I actually forgot that one...oh, well).
Lol, we learned all those four today! Odd, but I remember what a linear pair is. It's two oposite rays( A line ) and a ray with its end point on one of the rays. Only one of the third ray's points lays on the ray, and that is it's end point.

Now I know I'm not a good teacher, so this is what I said, if it came out too retarded sounding.

http://img246.imageshack.us/img246/4086/untitleduf4.jpg

P.S. Video games are WAY more nerdy then math. Who the hell thinks math is nerdy? This is the first time I've ever heard that. If you're good at math, that means you're smart. If you're not, that means you're not as smart.

I hate it when people get jealous and start accusing people of things. Now, let's not start a fight. Just chill, guys. Imagine yourself in a freezer.

[Iconoclast]

CD, don't forget, also: A man and a woman equals what's in your parent's bedroom.:D Lol, we learned all those four today! Odd, but I remember what a linear pair is. It's two oposite rays( A line ) and a ray with its end point on one of the rays. Only one of the third ray's points lays on the ray, and that is it's end point.

Now I know I'm not a good teacher, so this is what I said, if it came out too retarded sounding.

http://img246.imageshack.us/img246/4086/untitleduf4.jpg

P.S. Video games are WAY more nerdy then math. Who the hell thinks math is nerdy? This is the first time I've ever heard that. If you're good at math, that means you're smart. If you're not, that means you're not as smart.

I hate it when people get jealous and start accusing people of things. Now, let's not start a fight. Just chill, guys. Imagine yourself in a freezer.Oh, yeah. See, that's what I THOUGHT a linear pair was, but I said, nah, it couldn't be, so I just assumed I had forgot. The reason I thought it wouldn't be is that I thought that's what SUPPLEMENTARY angles are. If you noticed in your above image, linear pair angles add up to 180 degress. Supplementary angles also add up to 180 degrees. But if I was right, then what the hell is the difference between the two?

I'd rather start a math forum. WAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAY too much math that I learned to be discussing in a single thread. Math is too huge for just a thread. I can even get math involved in programming and stuff.

[Crazed Dragon]

I have moved this thread to the seinces/technolgy forum as math is a form of seinces anyways, so yeah get on with your brainy math things...

[recab2]

ok what i want to know is how can you justify using something that doesn't exist to factor an equation. for example, some equations cannot be factored, so they us an i in the factoring. i is the square root of -1, whcih does not exits. therefore, isn;t it logical for one to include that if i is needed, the equation cannot be factored.

[mudlord]

Math is too huge for just a thread. I can even get math involved in programming and stuff.

Easy to do. Why don't you do it? Or give us a example?

Here's mine, and its a practical example how most cel shading works....

Cel Shading 101

1) Work out the lighting by normal vectors (pixel_color = texture_map[(N dot L)]
(where "N" is the normal vector and "L" is the ray of light. Notice how there is what is known as a dot product by multiplying the normal vector and the light values (light vectors). The dot product between the two is the cosine of the angle between them)
2) the "texture_map" is a collection of 16 colours, and these colours correspond to the angle (dot product).
3) Then we use these texture maps to do back-face culling, for the outlines (really noticable black lines)
4) PROFIT!

[godgryphon]

Great method, im not very good at math, but know it is extremely important, i just wish I had someone to tutor me... Anyways, I use cell shading alot, im working on a few 3d projects at the moment.

[ridley]

icono ever done trigonometry?

[Iconoclast]

No, I can't take the class just yet, but I can school everyone here at geometry. The only exception to that is triangle and angle/segment bisector constructions. Those were a waste of my time, and even if I ever did how to learn them, I never remembered.

[Iconoclast]

That covers a lot of complex shapes, but it doesn't cover so much two-dimensional material. Triangles, for example, were hardly illustrated in the above diagram. They could've wrote that diagram about eight inches longer showing the construction of of medians, altitudes, perpendicular bisectors, angle bisectors, centroids, orthocenters, incenters and the circumcenters of a triangle. Even such a simple shape, a three-sided polygon, a triangle, has a lot of math to learn. Not to mention, their universal appearance in acute, right, obtuse and equiangular and equilateral triangles.

[Kit]

1) Work out the lighting by normal vectors (pixel_color = texture_map[(N dot L)]
(where "N" is the normal vector and "L" is the ray of light. Notice how there is what is known as a dot product by multiplying the normal vector and the light values (light vectors). The dot product between the two is the cosine of the angle between them)
2) the "texture_map" is a collection of 16 colours, and these colours correspond to the angle (dot product).
3) Then we use these texture maps to do back-face culling, for the outlines (really noticable black lines)
4) ???
5) PROFIT!

Fixed. If you're going to do the "PROFIT!" thing, you must do it right. :)

[mudlord]

Thanks for fixing that :). Next stop...HDR...

[mudlord]

Okay, a completely practical example..Quadratic Equations in C++:


#include <iostream>
#include <math.h>
using namespace std;

void one(){

float a = 0.0; //here we declare the variables and use float because we
float b = 0.0; //are dealing with square roots
float c = 0.0;
float x1 = 0.0;
float x2 = 0.0;
float x3 = 0.0;
float x4 = 0.0;

//this section gets user input and displays message
cout << "Enter the coefficients a , b , c for equation in the form ax^ + bx + c = 0:\n";
cout << "Enter value for a:\n";
cin >> a;
cout << "Enter value for b:\n";
cin >> b;
cout << "Enter value for c:\n";
cin >> c;

//are all the coefficients 0? if so both roots are 0
if(a == 0 && b == 0 && c == 0){
x1 = 0;
x2 = 0;
cout << "The roots are:" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}

//is c the only non-zero number? if so tell the user
if(a == 0 && b == 0 && c != 0){
c = c;
cout << "There are no roots" "\n"
<< "c = " << c << "\n";
}

if(a == 0 && b != 0 && c !=0){
cout << "The values entered do not make a quadratic expression" "\n"
<< "x = " << -c/b << "\n";
}

//if b is zero and c is zero tell user
if(a == 0 && b != 0 && c == 0){
x1 = 0;
x2 = 0;
cout << "The roots are:" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}

if(a != 0 && b == 0 && c == 0){
x1 = 0;
x2 = 0;
cout << "The values entered result in ax^= 0; so both roots are 0" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}

// solve linear equation
if(a != 0 && b != 0 && c == 0){
x1 = 0;
x2 = -b/a;
cout << "The roots are:" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}


if(a < 0 && b == 0 && c < 0){

x1 = -b/(2*a);
x4 = (b*b)-(4*a*c);
x4 = -x4;
x2 = sqrt(x4)/(2*a);
x3 = -sqrt(x4)/(2*a);


cout << "The roots are not real numbers:" "\n"

<< "x1 =" << x1 << " + " << x2 << " * i " << "\n"
<< "x2 =" << x1 << " + " << x3 << " * i " << "\n";

}

if(a > 0 && b == 0 && c > 0){

x1 = -b/(2*a);
x4 = (b*b)-(4*a*c);
x4 = -x4;
x2 = sqrt(x4)/(2*a);
x3 = -sqrt(x4)/(2*a);


cout << "The roots are not real numbers:" "\n"

<< "x1 =" << x1 << " + " << x2 << " * i " << "\n"
<< "x2 =" << x1 << " + " << x3 << " * i " << "\n";



}

if(a > 0 && b == 0 && c < 0){

x1 = (-b + (sqrt(pow(b,2)-(4*a*c))))/(2*a);
x2 = (-b - (sqrt(pow(b,2)-(4*a*c))))/(2*a);

cout << "The roots are:" "\n"
<< "x1 = "<< x1 << " , " << "x2 = "<< x2 << "\n";
}
if(a < 0 && b == 0 && c > 0){

x1 = (-b + (sqrt(pow(b,2)-(4*a*c))))/(2*a);
x2 = (-b - (sqrt(pow(b,2)-(4*a*c))))/(2*a);

cout << "The roots are:" "\n"
<< "x1 = "<< x1 << " , " << "x2 = "<< x2 << "\n";
}


if(a != 0 && b != 0 && c != 0 && (4*a*c) <= pow(b,2)){


x1 = (-b + (sqrt(pow(b,2)-(4*a*c))))/(2*a);
x2 = (-b - (sqrt(pow(b,2)-(4*a*c))))/(2*a);

cout << "The roots are:" "\n"
<< "x1 = "<< x1 << " , " << "x2 = " << x2 << "\n";
}


if(a != 0 && b != 0 && c != 0 && (4*a*c)> pow(b,2)){


x1 = -b/(2*a);
x4 = (b*b)-(4*a*c);
x4 = -x4;
x2 = sqrt(x4)/(2*a);
x3 = -sqrt(x4)/(2*a);


cout << "The roots are not real numbers" "\n"

<< "x1 =" << x1 << " + " << x2 << " * i " << "\n"
<< "x2 =" << x1 << " + " << x3 << " * i " << "\n";




}
return;

}


void two(){
char c ;
cout << "Press c and then Enter to continue...." "\n";
cin >> c;
for(;;){
if ( c ){
break;
}
}

cout << "Done" "\n";

}

int main(){
one();
two();
return 0;
}