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gamer66618

274 posts

Nomad

Posted November 19, '11 4:09pm UTC

I like math(s?)...

I'm English. In USA you say math, in England you say maths or mathematics and statistics etc.

There really is no such thing as suction. Moving on...

I know I was just trying to describe the movement of air molecules from an area of high concentration to an area of low concentration inside the lungs when the pressure changes this causes the air to move in. You're right, it isn't suction.

Yeah. I did surds and I also do quadratics and the discriminant. You cannot reach a normal answer on a calculator if you try to square root a negative. However odd number roots (e.g. 3, 5, 7, 9 etc.) do have real numbers that are negative, because if you times a number by itself it would be a negative timesed by a negative. Negatives timesed together give positives. However if you times that by another negative it becomes negative, however if you times it by yet another negative you end up with a positive. Therefore even number roots don't have real number negatives but odd number roots do. I know that from AS-Level maths.

This is where things get interesting: in order to keep track of complex numbers, we don't use a number line like we do for real numbers, but a plane (called the complex plane). We represent each point z=x+iy on the plane by its x and y coordinates, just like we would if we were graphing an equation of one variable onto a real graph.

Did not know that...

Is that degree level? Did you get that off wikipedia, or did you already know it? My maths teacher has done a degree in Mathematics and Statistics and she said that she's worked with imaginary roots and numbers etc. 3 dimensional, eh?

When we do this, we see that all lines through the origin (the point 0,0) on the plane are mapped to circles on the sphere that intersect the north and south poles, IE longitudes.

THIS is the interesting part (I SWEAR). So, the circles intersect each other twice (once at each pole) but the lines only appear to intersect each other once. Because the function we are using is conformal, we know that every intersection on the sphere must be mapped from an intersection on the plane. So, where is the missing intersection on the plane? I'll tell you! It is at the POINT at infinity! You see, in the complex plane, there is no difference between "negative" infinity and positive infinity. I mean, what would infinitely imaginary mean, anyway? So, we consider all the different kinds of complex infinity to just be one point on the plane that all lines must pass through

Wow this is beyond my knowledge... You sure this is not degree or at least advanced level?

So, all non-parallel lines in the complex plane intersect twice, and all parallel lines intersect once. Crazy!

Interesting.

*The interesting this about this definition is that imaginary numbers have no inherit concept of size or polarity (like positive versus negative) the way real numbers do. Think about it: what is i squared -1. But, What is negative i squared? -1. (just like how -2 x -2=4). So, what is the square root of -1? both i and -i. So, every time we define i, we don't know if we are getting negative i or positive i. So we can't say things like -i < i, since, we don't actually know which is which!

Okay now that bit I get. If you are operating with imaginary numbers and roots, then how do you know that it is positive or negative therefore how can you polarise? This is quite complex, just like anything divided by 0 could equal either positive or negative infinite! OMG! So therefore it is difficult to quantify because you don't know when working with imaginary numbers and roots whether you are adding a negative or a positive with a negative or a positive number? More importantly it gets more difficult to determine if you have a negative decimal imaginary number; I'm fairly sure this is degree level, and therefore beyond my expertise, but I don't know because I don't do further maths...

[quote]I like math(s?)... [/quote] I'm English. In USA you say math, in England you say maths or mathematics and statistics etc.\r\n\r\n[quote]There really is no such thing as suction. Moving on...[/quote] I know I was just trying to describe the movement of air molecules from an area of high concentration to an area of low concentration inside the lungs when the pressure changes this causes the air to move in. You're right, it isn't suction.\r\n\r\nYeah. I did surds and I also do quadratics and the discriminant. You cannot reach a normal answer on a calculator if you try to square root a negative. However odd number roots (e.g. 3, 5, 7, 9 etc.) do have real numbers that are negative, because if you times a number by itself it would be a negative timesed by a negative. Negatives timesed together give positives. However if you times that by another negative it becomes negative, however if you times it by yet another negative you end up with a positive. Therefore even number roots don't have real number negatives but odd number roots do. I know that from AS-Level maths. [quote]This is where things get interesting: in order to keep track of complex numbers, we don't use a number line like we do for real numbers, but a plane (called the complex plane). We represent each point z=x+iy on the plane by its x and y coordinates, just like we would if we were graphing an equation of one variable onto a real graph.[/quote] Did not know that...\r\n\r\nIs that degree level? Did you get that off wikipedia, or did you already know it? My maths teacher has done a degree in Mathematics and Statistics and she said that she's worked with imaginary roots and numbers etc. 3 dimensional, eh?\r\n\r\n[quote]When we do this, we see that all lines through the origin (the point 0,0) on the plane are mapped to circles on the sphere that intersect the north and south poles, IE longitudes.\r\n\r\nTHIS is the interesting part (I SWEAR). So, the circles intersect each other twice (once at each pole) but the lines only appear to intersect each other once. Because the function we are using is conformal, we know that every intersection on the sphere must be mapped from an intersection on the plane. So, where is the missing intersection on the plane? I'll tell you! It is at the POINT at infinity! You see, in the complex plane, there is no difference between "negative" infinity and positive infinity. I mean, what would infinitely imaginary mean, anyway? So, we consider all the different kinds of complex infinity to just be one point on the plane that all lines must pass through[/quote] Wow this is beyond my knowledge... You sure this is not degree or at least advanced level? [quote]So, all non-parallel lines in the complex plane intersect twice, and all parallel lines intersect once. Crazy![/quote] Interesting.[quote]*The interesting this about this definition is that imaginary numbers have no inherit concept of size or polarity (like positive versus negative) the way real numbers do. Think about it: what is i squared -1. But, What is negative i squared? -1. (just like how -2 x -2=4). So, what is the square root of -1? both i and -i. So, every time we define i, we don't know if we are getting negative i or positive i. So we can't say things like -i < i, since, we don't actually know which is which![/quote] Okay now [i]that[/i] bit I get. If you are operating with imaginary numbers and roots, then how do you know that it is positive or negative therefore how can you polarise? This is quite complex, just like anything divided by 0 could equal either positive or negative infinite! OMG! So therefore it is difficult to quantify because you don't know when working with imaginary numbers and roots whether you are adding a negative or a positive with a negative or a positive number? More importantly it gets more difficult to determine if you have a negative decimal imaginary number; I'm fairly sure this is degree level, and therefore beyond my expertise, but I don't know because I don't do further maths...

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gamer66618

274 posts

Nomad

Posted November 19, '11 4:12pm UTC

Wait, wait, wait... Do you do science and maths or just maths? I'm confused...

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aknerd

1,416 posts

Peasant

Posted November 19, '11 4:39pm UTC

I'm English. In USA you say math, in England you say maths or mathematics and statistics etc.

That's interesting. I mean, we say statisticS and mathematicS too, so really we should say maths (we do say stats, by the way, and not stat). But it sounds weird... anyway.

Is that degree level? Did you get that off wikipedia, or did you already know it?

Its something I learned/figured out* in my complex variables class, which is pre-graduate level class. I am currently over halfway done with completing my Math major in college. Wikipedia can sometimes be helpful with math, but often their proofs of concepts are very bad, or they assume that the reader has a PhD in math.

*in higher level math classes you have to figure out as many things as you are taught. Which can be both rewarding and annoying.

Wow this is beyond my knowledge.

Well, maybe! But I don't think it is beyond your understanding. If you think of the sphere as a ball placed on the origin of the plane, and then wrapping the plane around the sphere, it kind of makes sense. All of the "edges" of the plane (ie the points infinitely far from zero) would meet at the top of the ball.

Notes that this also implies that all lines can be thought of as circles through infinity.

More importantly it gets more difficult to determine if you have a negative decimal imaginary number

What's really weird is when you compare real numbers and pure imaginary numbers.

For instance, which is greater: i, or 1?

For reasons such as these, we don't try to compare sizes of complex numbers. Instead, we compare sizes of their absolute values, which is just their distance from the origin in the complex plane (just like how with real numbers the absolute value is the distance from zero on the number line). Of course, this mean that all complex numbers on a circle with the same radius centered at the origin have the same absolute size.

(so, to answer my own question, |i| = |1| = |-1| = |-i|).

[quote]I'm English. In USA you say math, in England you say maths or mathematics and statistics etc.[/quote]\r\nThat's interesting. I mean, we say statisticS and mathematicS too, so really we should say maths (we do say stats, by the way, and not stat). But it sounds weird... anyway.\r\n\r\n[quote]Is that degree level? Did you get that off wikipedia, or did you already know it? [/quote]\r\nIts something I learned/figured out* in my complex variables class, which is pre-graduate level class. I am currently over halfway done with completing my Math major in college. Wikipedia can sometimes be helpful with math, but often their proofs of concepts are very bad, or they assume that the reader has a PhD in math. \r\n\r\n*in higher level math classes you have to figure out as many things as you are taught. Which can be both rewarding and annoying.\r\n\r\n[quote]Wow this is beyond my knowledge.[/quote]\r\nWell, maybe! But I don't think it is beyond your [i]understanding[/i]. If you think of the sphere as a ball placed on the origin of the plane, and then wrapping the plane around the sphere, it kind of makes sense. All of the "edges" of the plane (ie the points infinitely far from zero) would meet at the top of the ball.\r\n\r\nNotes that this also implies that all lines can be thought of as circles through infinity. \r\n\r\n[quote]More importantly it gets more difficult to determine if you have a negative decimal imaginary number[/quote]\r\n\r\nWhat's really weird is when you compare real numbers and pure imaginary numbers.\r\n\r\nFor instance, which is greater: i, or 1? \r\n\r\nFor reasons such as these, we don't try to compare sizes of complex numbers. Instead, we compare sizes of their absolute values, which is just their distance from the origin in the complex plane (just like how with real numbers the absolute value is the distance from zero on the number line). Of course, this mean that all complex numbers on a circle with the same radius centered at the origin have the same absolute size. \r\n\r\n(so, to answer my own question, |i| = |1| = |-1| = |-i|).

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gamer66618

274 posts

Nomad

Posted November 19, '11 5:06pm UTC

That's interesting. I mean, we say statisticS and mathematicS too, so really we should say maths (we do say stats, by the way, and not stat). But it sounds weird... anyway.

Yeah, I agree. We say stats too as well as statistics and algorithms.

Its something I learned/figured out* in my complex variables class, which is pre-graduate level class. I am currently over halfway done with completing my Math major in college. Wikipedia can sometimes be helpful with math, but often their proofs of concepts are very bad, or they assume that the reader has a PhD in math.

*in higher level math classes you have to figure out as many things as you are taught. Which can be both rewarding and annoying.

Yeah I don't do variables. I do less complex stuff like integration, differentiation, quadratic, cubics and other polynomials, circles, co-ordinate geometry and surds. BTW: very good on figuring that out! I'd've never've guessed that; I'd've been had to've been taught that, no?

Well, maybe! But I don't think it is beyond your understanding. If you think of the sphere as a ball placed on the origin of the plane, and then wrapping the plane around the sphere, it kind of makes sense. All of the "edges" of the plane (ie the points infinitely far from zero) would meet at the top of the ball.

Yeah, weirdly I heard that about theoretical physics at and beyond PhD level using that kind of advanced mathematics in their formidably difficult physics equations (you gotta be good at maths if you wanna be good at physics, ya know?...). That's kinda beyond my knowledge and probably beyond my understanding as well. I prefer biology and I prefer stats to variables within maths (hence why I picked Mathematics and Statistics instead of Decision Maths because even though they otherwise have the same modules they have the last exam as optional between Decision Maths (algorithms, variables etc.) and statistics (exponent function, other things etc.)). Circles through infinity? Hmm...
I have done 3 dimensional coordinate values, but never spherically so. I've done circles and 3D affects, but never combined! As far as I've ever gotten was drawing cuboids! Still a sphere is
area=(2/3 pi r)cubed (i.e. the radius multiplied by pi multiplied by 2/3 all cubed). So you could probably work out the area of the sphere even if it circles round infinite.

For instance, which is greater: i, or 1?

For reasons such as these, we don't try to compare sizes of complex numbers. Instead, we compare sizes of their absolute values, which is just their distance from the origin in the complex plane (just like how with real numbers the absolute value is the distance from zero on the number line). Of course, this mean that all complex numbers on a circle with the same radius centered at the origin have the same absolute size.

(so, to answer my own question, |i| = |1| = |-1| = |-i|).

Well, yeah. I mean if you try to compare x squared to x cubed you not gonna get an answer, know what I mean? You need to figure out the values they stand for to compare them (like 4 and 7 or something...). And you can't compare ionisation energies because of the extreme differences between them; plotting a graph with appropriate scales would be a nightmare! But if you find the "log." (i.e. logarithm) of the ionisation energies, you can plot those points instead and see that the differences lie between changes in the energy shells as one shell is removed, you're closer to the nucleus and the attraction is more and the shielding is less. You learn that sorta stuff as AS-Level Chemistry. So therefore you just compare the distances from the origin. That makes sense...

[quote]That's interesting. I mean, we say statisticS and mathematicS too, so really we should say maths (we do say stats, by the way, and not stat). But it sounds weird... anyway.[/quote] Yeah, I agree. We say stats too as well as statistics and algorithms. [quote]Its something I learned/figured out* in my complex variables class, which is pre-graduate level class. I am currently over halfway done with completing my Math major in college. Wikipedia can sometimes be helpful with math, but often their proofs of concepts are very bad, or they assume that the reader has a PhD in math.\r\n\r\n*in higher level math classes you have to figure out as many things as you are taught. Which can be both rewarding and annoying.[/quote] Yeah I don't do variables. I do less complex stuff like integration, differentiation, quadratic, cubics and other polynomials, circles, co-ordinate geometry and surds. BTW: very good on figuring that out! :) I'd've never've guessed that; I'd've been had to've been taught that, no? [quote]Well, maybe! But I don't think it is beyond your understanding. If you think of the sphere as a ball placed on the origin of the plane, and then wrapping the plane around the sphere, it kind of makes sense. All of the "edges" of the plane (ie the points infinitely far from zero) would meet at the top of the ball.[/quote] Yeah, weirdly I heard that about theoretical physics at and beyond PhD level using that kind of advanced mathematics in their formidably difficult physics equations (you gotta be good at maths if you wanna be good at physics, ya know?...). That's kinda beyond my knowledge and probably beyond my understanding as well. I prefer biology and I prefer stats to variables within maths (hence why I picked Mathematics and Statistics instead of Decision Maths because even though they otherwise have the same modules they have the last exam as optional between Decision Maths (algorithms, variables etc.) and statistics (exponent function, other things etc.)). Circles through infinity? Hmm...\r\n I have done 3 dimensional coordinate values, but never spherically so. I've done circles and 3D affects, but never combined! As far as I've ever gotten was drawing cuboids! Still a sphere is \r\narea=(2/3 pi r)cubed (i.e. the radius multiplied by pi multiplied by 2/3 all cubed). So you could probably work out the area of the sphere even if it circles round infinite.  [quote]For instance, which is greater: i, or 1?\r\n\r\nFor reasons such as these, we don't try to compare sizes of complex numbers. Instead, we compare sizes of their absolute values, which is just their distance from the origin in the complex plane (just like how with real numbers the absolute value is the distance from zero on the number line). Of course, this mean that all complex numbers on a circle with the same radius centered at the origin have the same absolute size.\r\n\r\n(so, to answer my own question, |i| = |1| = |-1| = |-i|).[/quote] Well, yeah. I mean if you try to compare x squared to x cubed you not gonna get an answer, know what I mean? You need to figure out the values they stand for to compare them (like 4 and 7 or something...). And you can't compare ionisation energies because of the extreme differences between them; plotting a graph with appropriate scales would be a nightmare! But if you find the "log." (i.e. logarithm) of the ionisation energies, you can plot those points instead and see that the differences lie between changes in the energy shells as one shell is removed, you're closer to the nucleus and the attraction is more and the shielding is less. You learn that sorta stuff as AS-Level Chemistry. So therefore you just compare the distances from the origin. [i]That[/i] makes sense...

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gamer66618

274 posts

Nomad

Posted November 19, '11 6:10pm UTC

Did you know that the densest gas at room temperature and pressure is radon which is so dense that the atoms are unstable and fall apart easily emitting radiation and causing it to be radioactive. A radioactive gas? Who on earth has ever heard of such a thing? It is the only one! They thought that ununoctium was a noble gas but it turned out to be a solid due to relativistic effects. Even though it is a group 18 element, it is a solid! Ununoctium has only ever had 3 or possibly 4 atoms ever made. It has been made by nuclear bombardment of Krypton and lead atoms to form ununoctium, the heaviest element created so far. It is the only group 18 element created via nuclear synthesis. Mercury is the heaviest liquid there is. It is the only transition metal at room temperature and pressure. It has the highest surface tension and even iron will float on its surface as well as other metals like copper. The densest solid is plutonium. The densest solid that there could be is unsepttrium but it hasn't be synthesised yet and may not even be possible to make. The densest so far made is unbioctium but it has only had very few atoms made so far. The densest solid so far made is Einsteinium. Fermium is the lightest which cannot be seen as only atoms of it have been made; not enough to be seen. Anything after that only exists as atoms not solids so therefore not enough has been made to make a solid. So anything after Einsteinium is not enough to make a solid yet. So the heaviest solid is Einsteinium and the heaviest atom is unbioctium and the heaviest hypothetical elemental atom is unsepttrium and the heavist liquid is mercury and the heaviest gas is radon. This is all based on when it is at room temperature and pressure.

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gamer66618

274 posts

Nomad

Posted November 19, '11 6:25pm UTC

Sorry! I meant ununoctium, not unbioctium!

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gamer66618

274 posts

Nomad

Posted November 19, '11 6:31pm UTC

Plutonium is the heaviest natural element and Einsteinium is the heaviest synthetic solid. Fermium onwards is only atoms in very small quantity. Ununoctium being the heaviest of this type. The heaviest hypothetical element is unsepttrium.

Any questions about science or mathematics?

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gamer66618

274 posts

Nomad

Posted November 19, '11 7:46pm UTC

Yeah, I want more people to post things on this thread because I don't want it going necro, know what ah'm sayin, eh?

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gamer66618

274 posts

Nomad

Posted November 21, '11 3:12pm UTC

Fine! Why won't anybody post anything!?

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Kasic

5,546 posts

Jester

Posted November 21, '11 3:29pm UTC

Fine! Why won't anybody post anything!?

There's no point or discussion. You just keep posting random facts about math/science. Why would anyone post? What would they do? While it's not off topic or spam, it's the equivilant of reading a science textbook that jumps off in random directions. So...if you want to have a discussion, provide a topic, not just random facts.

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gamer66618

274 posts

Nomad

Posted November 21, '11 4:06pm UTC

There's no point or discussion. You just keep posting random facts about math/science. Why would anyone post? What would they do? While it's not off topic or spam, it's the equivilant of reading a science textbook that jumps off in random directions. So...if you want to have a discussion, provide a topic, not just random facts.

God, you're so argumentative. This is a discussion thread not a debate thread, plus I'm inviting people to post their own topics based on mathematical and scientific things and there ain't anybody intelligent enough to think of anything or at least they can't think of anything off the top of their head; do you have anything to add or a topic to discuss about mathematics or science? If not, then get the hell off my thread and stop spamming!

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gamer66618

274 posts

Nomad

Posted November 21, '11 4:28pm UTC

Isn't there anyone out of the 1.8 million users that wanna post something on maths or science just to get it off your chest? Come on... Please?

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gamer66618

274 posts

Nomad

Posted November 21, '11 5:10pm UTC

It is impossible to sustain this thread if people don't post their knowledges of science and maths. Please post something! I've run out of ideas! I need new content! NOW!

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gamer66618

274 posts

Nomad

Posted November 21, '11 5:34pm UTC

Okay, I understand that nobody is intelligent to understand a single blind thing about maths and science because you're all idiots, but I still see no reason why not to post questions about it? Or are you too simple to do that even?

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gamer66618

274 posts

Nomad

Posted November 21, '11 5:49pm UTC

Maybe we're just not interested. Many people are in school now anyways.

LOL! I'm an adult and I don't go to school! And today is a teacher's training day, so I don't have college today either. [/quote]There's also a Tachyon, if I recall correctly[quote] Don't know; haven't done subatomic particles, but that isn't on the syllabus, only neutrinos, neutrons, electrons, protons, meuons, mesons, quarks, anitquarks etc.

Care to explain further?

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