The Math and Science Thread

[BronyPony 575]

WELCOME TO THE MATH AND SCIENCE THREAD

 

Are you a fan of mathematics and science? Do you want to present things you have discovered in either field? You can post it here. Or, if you want to, you can post whatever you find fascinating in these two fields(these two fields include many more fields that exist).

 

Well, to start, I would like to present MY discoveries in mathematics.

 

The function of e^x, or simply the constant of e, has many special properties that makes it a unique function. For example, the derivative of e^x is simply itself as its own derivative. This has lead to one particular discovery about the connection between the function e^x and the Collatz conjecture, which is the following.

This is what is called a Lambda Function of the Aleph Derivative. This takes two functions, like in the Collatz conjecture, and makes an equation to describe the trend of the output of the rules, such as found in the Collatz conjecture. More specifically, it takes the two concepts, which are the Aleph Integral and the derivative of the function and its inverse, and combines them together to form a function to describe the trend of the Collatzian ratio and the effect from using the rules found in the Collatz conjecture. For example, here is what describes the parameters of the Collatz conjecture and the function of the trends.

This means that the function that describes the trend of growth for the parameters of the Collatz conjecture is e^(x/2). This means the trend will grow exponentially in terms with the natural constant e.

The mean, or average, of all similar trends will eventually become the function of e^x. This means that all values of n for the Collatz parameters will end up producing a finitely sized Hailstone sequence. This means that the Collatz conjecture must be true because it will remain on a finite portion of the function of e^x.

Then the question becomes what will happen when dealing with Collatzian ratios that becomes polynomial equations or involve sine or cosine functions. For example, here is a graph that would represent the output of these kind of functions in a Collatzian ratio.

Based on the conclusion of the exponential function, the conclusion that can be made from this type of function is that it would be a looping sequence. This means that it would never approach 1. There are also other type of functions that would reach this conclusion, but this is a very simple example of this.

I will continue research on this. Thanks for reading.

 

If you want more information on this interesting finding, just go here: http://blogs.scienceforums.net/mysteriesofmath/

 

Alright, post away!

Edited December 12, 2013 by BronyPony

[Rayalicious 435]

Oh wow, Coincidence I guess, trimester 2 just began, and we've been introduced to integrals and Ln functions, soon we will be doing exponential(but i started by myself cause it looked fun ). PS: I Love math :3
And true the exponential is a very unique function(other than the name specifying it's variation), noting that it is the inverse of an Ln function(which cannot be negative) but i guess you seem pretty advanced in this field , we have yet to take integration by part which is long and hard, but pretty interesting . (Thumbs up for this thread )

Now: exponential function are used in multiple communication fields, for instance: Limiting an antenna's emission only to a straight hallway, excluding all adjacent rooms, in this case the usage of an exponential is necessary as it reshapes the signal's from a circular or globe like emission to a straight line. Will be keeping up with this thread

[BronyPony 575]

Oh wow, Coincidence I guess, trimester 2 just began, and we've been introduced to integrals and Ln functions, soon we will be doing exponential(but i started by myself cause it looked fun ). PS: I Love math :3

And true the exponential is a very unique function(other than the name specifying it's variation), noting that it is the inverse of an Ln function(which cannot be negative) but i guess you seem pretty advanced in this field , we have yet to take integration by part which is long and hard, but pretty interesting . (Thumbs up for this thread )

 

Now: exponential function are used in multiple communication fields, for instance: Limiting an antenna's emission only to a straight hallway, excluding all adjacent rooms, in this case the usage of an exponential is necessary as it reshapes the signal's from a circular or globe like emission to a straight line. Will be keeping up with this thread

That is pretty interesting. With antenna emissions, there are also ways to expand the array of the distance that information travels by using fractal designs.

 

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=997888&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F74%2F21527%2F00997888

 

I find that the natural exponential function and the natural logarithm has an important role in equations, especially when proving the Collatz conjecture. It shows the relationship between ratios that are included in Collatz Theory(mathematical research I have been working on). It gives predictions to global maximums in hailstone sequences, which is pretty interesting. It also gives predictions of time iterations based on the numbers being used.

 

I feel that these two concepts seem to show a ratio between the numbers of equations. More would have to be researched, but they are definitely important concepts in the simply known algebra. 

Edited December 12, 2013 by BronyPony

[Wayzer 1,418]

Is it weird that I kinda suck in math and be really good in physics at the same time? I always thought of it as weird, but physics is just so much simpler.

[BronyPony 575]

Is it weird that I kinda suck in math and be really good in physics at the same time? I always thought of it as weird, but physics is just so much simpler.

It really depends whether your mind works with symbols or not. You may work well with the visual understandings of a particular topic, but symbolically it may be difficult to understand the language.

[Legacy Dash 439]

Nooooo! Maths. My brain hurts.

That looks so confusing! Arg!

 

You seem to be a pretty skillful mathematician though. Good job! 

[BronyPony 575]

Nooooo! Maths. My brain hurts.

That looks so confusing! Arg!

 

You seem to be a pretty skillful mathematician though. Good job! 

Mathematics is simple, but being able to interpret the symbolic language is the difficulty.

 

The reason why it is better to represent certain ideas as symbols is due to the fact that English, and other languages, don't have the capabilities of explaining the topics with the words available. Once you begin to understand the symbols, it becomes easier to see what is actually being said. It just takes time to get used to the kind of structure of mathematical equations.

Well, in the time I have, I made part of a theorem meant for Collatz theory called the Collatz Theorem of Quadratic functions. It is the following:

 

Iff f(x) is quadratic, then integrate iff f(x) = g(x) * g^-1(x) <-inverse of g(x)

 

 

Where . With quadratic equations, the quadratic formula can be revised to fit this scenario, or theorem.

 

 

 

I am close to being able to find a way to find C for when a linear equation is integrated from a previous derivative.

[Commander Tangent 861]

Well considering my name, I  bet you can all guess what I think of Math xD. We just started integrating physics into our engineering course. 

[BronyPony 575]

Well considering my name, I  bet you can all guess what I think of Math xD. We just started integrating physics into our engineering course. 

I noticed.   You must be the result of the derivative of a curve function. 

[Lonely 93]

oh my god   this math is frying my brain   I don't like it   sorry I just don't umderstand it

[BronyPony 575]

oh my god   this math is frying my brain   I don't like it   sorry I just don't umderstand it

Welcome my friend. There is more where that came from. I wonder if anyone will bring up topology...

[Nerdy Luigi 2,065]

Wow. I don't know that yet. Because I'm just an algebra II student. But I do happen to be good in certain areas of mathematics. But those areas are easy for these future engineers and college professors. Which, I am not one. But I do like chemistry... Greatest simple math in the history of math, particularly the part everyone says is quite impassable, the balancing of a chemical equation (come on Texas, this should be WAY too easy!)

Edited December 12, 2013 by Twilight Sniper

[BronyPony 575]

Wow. I don't know that yet. Because I'm just an algebra II student. But I do happen to be good in certain areas of mathematics. But those areas are easy for these future engineers and college professors. Which, I am not one. But I do like chemistry... Greatest simple math in the history of math, particularly the part everyone says is quite impassable, the balancing of a chemical equation (come on Texas, this should be WAY too easy!)

There as been some recent discoveries in chemistry related to the properties of valence electrons. I'll find the article.

[valete 195]

Math!! 

 

Oh dear. Every time I see math stuffs, I'd usually get curious or interested...but that's only if I can comprehend the math being discussed. 

 

Math can (sometimes) be fun to mess around with when you're not being pushed to learn it fast inside a classroom. 

 

Actually, I made my own sample equation a few months ago, and it was (kind of) related to our lesson at the time! 

It isn't exactly what I'd call academic, though. 

 

 

Here it is: 

 

If f(x) = derpy - (x), then what is f(muffins)? 

[Wayzer 1,418]

Math!! 

 

Oh dear. Every time I see math stuffs, I'd usually get curious or interested...but that's only if I can comprehend the math being discussed. 

 

Math can (sometimes) be fun to mess around with when you're not being pushed to learn it fast inside a classroom. 

 

Actually, I made my own sample equation a few months ago, and it was (kind of) related to our lesson at the time! 

It isn't exactly what I'd call academic, though. 

 

 

Here it is: 

 

If f(x) = derpy - (x), then what is f(muffins)? 

I agree, I like maths but I hate math classes. You have to learn things so fast.

[Commander Tangent 861]

I love math, because everything in math runs by a logic system that, if you know what you are doing, can be kinda easy.

 

But yeah, most math classes go way to fast T_T.

[~Lawful Haze~ 173]

Not a fan of straight maths.

 

HUGE fan of physics.

 

Go figure.

[Sapana 66]

I love math, and I was pretty good at the basics. Calc II in college was where I started struggling. Understood the principles, but had trouble applying them to actual problems. Same with Chemistry and Physics. Fascinating stuff, but I wasn't the greatest. Biology was my forte. 

[Ac3xAssasin 453]

I honestly enjoy physics instead more than math, because it is an application of what you learn in math.  Here's something we learned recently in my physics class.  My dream right now is to become an Astrophysicist (The workings of space have always facinated me) 

 

How to derive an equation for Orbital Period (T) of a circular orbit based on Newton's law of Universal Gravitation.

 

We start with the famous equation F=ma

 

since we know that the only force acting on a satellite is gravity and it is in circular motion we can expand the equation into 

 

GmM/r^2 = mv^2/r

 

little m cancels out

 

since we know v =  2πr/T we can plug it into the equation and get

 

GM/r^2 = 4π^2r^2/T^2r

 

cancel the r on the bottom to get

 

GM/r^2 = 4π^2r/T^2

 

multiply both sides by r^2 to get 

 

GM = 4π^2r^3/T^2

 

some rearrainging later and you get 

 

T^2 = 4π^2r^3/GM

 

Take the square root and you are left with

 

T =  2π√r^3/GM

 

and walla! we have a simple equation for orbital period of a circular orbit.  Notice the T^2 and r^3 which corresponds directly to Kepler's law of periods stating the T^2 of any orbit is proportional to its r^3.

 

P.S. I didn't actually learn to do this in physics class I tried one night when I was really bored and checked my outcome on the interwebz.

Edited December 13, 2013 by aceassasin

[BronyPony 575]

I honestly enjoy physics instead more than math, because it is an application of what you learn in math.  Here's something we learned recently in my physics class.  My dream right now is to become an Astrophysicist (The workings of space have always facinated me) 

 

How to derive an equation for Orbital Period (T) of a circular orbit based on Newton's law of Universal Gravitation.

 

We start with the famous equation F=ma

 

since we know that the only force acting on a satellite is gravity and it is in circular motion we can expand the equation into 

 

GmM/r^2 = mv^2/r

 

little m cancels out

 

since we know v =  2πr/T we can plug it into the equation and get

 

GM/r^2 = 4π^2r^2/T^2r

 

cancel the r on the bottom to get

 

GM/r^2 = 4π^2r/T^2

 

multiply both sides by r^2 to get 

 

GM = 4π^2r^3/T^2

 

some rearrainging later and you get 

 

T^2 = 4π^2r^3/GM

 

Take the square root and you are left with

 

T =  2π√r^3/GM

 

and walla! we have a simple equation for orbital period of a circular orbit.  Notice the T^2 and r^3 which corresponds directly to Kepler's law of periods stating the T^2 of any orbit is proportional to its r^3.

 

P.S. I didn't actually learn to do this in physics class I tried one night when I was really bored and checked my outcome on the interwebz.

It becomes fascinating when people begin to manipulate the equations and realize and discover something new about our Universe. It also can become tiring because when I began working on string theory I was combing equations from Einstein's equations and the equations of quantum mechanics when I landed up with the equation E = √E, which is impossible because the energy is never equal to its self squared. Though I repeated the process of manipulation over and over again, I still got the same equation. I just left it alone and declared my hypothesis wrong because it was impossible to have that type of equation.

[Doc. Volt 2,561]

oh hello fellow... i really hate math but i had to study it in my engineering course... can i talk about cascade resonance from 2 Tesla coils as a way to wirelessy trasnport electric energy? Somepony are interested?

[BronyPony 575]

oh hello fellow... i really hate math but i had to study it in my engineering course... can i talk about cascade resonance from 2 Tesla coils as a way to wirelessy trasnport electric energy? Somepony are interested?

Talk about it any way you like. Welcome to the math and science thread. 

 

EDIT: I heard that they are developing a way to switch from our current way of transmitting energy from wires to tesla coils. However, last  time I remember, I thought they canceled the project for some reason.

 

 

In Calculus, limits are what approach a certain value of x without ever equaling the value of x. For example, the following would be a way limits work.

As seen in this limit, the value of x approaches infinity, which means that the solution to this problem is 0 because 1/? is equal to 0. This kind of concept would be what occurs with curvature limits, but in a different fashion. Before explaining curvature limits, here is an example of a curvature limit being applied to the Lambda Function of Derivatives.

In this case, the limit is merely an extension of the equation. It shows that the Lambda function is a curvature limit, where the function that is a result is the solution to the curvature limit. For a demonstration, here is an animation of what a curvature limit would look like.

The above animation is a result of the curvature limit of the Collatz parameters, with 1 being the reference frame and the value of n, or 27, being what is tested relative to 1.

Now, in the animation above, there were only Collatz numbers that were tested for iteration which means that Collatz numbers act as the compositions of this curvature limit. Here is the Hailstone sequence of 27 where the Collatz numbers are bolded.

{ 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91,274, 137,412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445,1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92,46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 }

This means that Collatz numbers have an important role in curvature limits. It also means that the derivative of a function and its inverse has a strong relevance to the curvature limit. There are many hypotheses, or conclusion, that can be made from this type of phenomena.

Here is another part of the discoveries I made in Collatz Theory. They are what are called curvature limits. It is similar to the regular limit except it deals with approaching a curve rather than approaching a certain value. It shows that there is a curvature limit for the Collatz conjecture. However, I am yet to make a mathematical test to see if something will approach a curvature limit or not. Once I develop this test then I can prove the Collatz conjecture.

Edited December 13, 2013 by BronyPony

[Doc. Volt 2,561]

Talk about it any way you like. Welcome to the math and science thread. 

 

EDIT: I heard that they are developing a way to switch from our current way of transmitting energy from wires to tesla coils. However, last  time I remember, I thought they canceled the project for some reason.

everything Tesla related will be cancelled trust me... i have some old books at the university wich one does not simple find... some awesome stuff... Schuman's resonance... actually it is a over-runnity system since the energy you get at the ed is more than what you used (well in theory) this is because you gather energy from the earth magnetif field, well let's just start how an easy Tesla coil wroks shall we?

 

LESSON 1: TRANSFORMATOR

 

You may all know what is a transformator, it is a really simple electric device wich "converts" the voltage from an input ALTERNATE current to an output with a different voltage but at the saem frequency... actually if you lover the volts you get higher amps and vice-versa, because the general power (volt X ampere) is equally in input and in output, so

 

V1 X A1 = V2 X A2

 

P1 = P2

 

 

the voltage drop or gain is related to the number of turns...

 

V1/number of turns1 = V2/number of turns2

 

if we have a coil and we put a direct current trough it we get nothing.. it will act like a wire...generating a costant magnetic field (it will act like a magnet)  but if we put an alternate current we will generate a changing magnetic field, this magnetic field can be "heard" by another coil, if the magnetic field is variable we can get a current inside this other coil, a cirrent that is trying to stop the magnetic field... actually a transformator is done by 2 coils, one in input and one as output, wired around a ferro.magnetic block

 

this is the first step (sorry for no formulas but i am tring to keep this simple)

Edited December 13, 2013 by Doc. Volt

[Ac3xAssasin 453]

There's only one thing wrong with this thread, it needs more physics!

 

Today we are going to prove Galileo's hypothesis that acceleration is uniform no matter the mass right with the conservation of energy.

 

Method 1: energy

 

If a person is standing at height h we know the GPE they posses is equal to

 

mgh

 

Based on the conservation of energy we can assume if this object fell from height h all the GPE becomes KE at the bottom

 

GPE = KE

mgh = 1/2mv^2

M cancels out and therefore velocity is not dependent and thus Galileo was correct.

Edited December 13, 2013 by aceassasin

[GenderIsAnIllusion 2,177]

*Reads OP*... *Jaw hits floor*

 

I just finished calc 2, and I understood exactly 1 thing you said. O_O