Maths- Gym for Brainiacs

vizkosity wrote:why, if not for the fact that it's true for all x, y, z?
the maximum isn't greater than 1/2, and in nowhere there is a complex factor in the simple expression. If it's not true for all x,y,z set that follows the constraint, then how is it wrong if there is only 1 factor of lambda available?

and thanks for the video :[ Although i expected something that is classier
not really a fan of slutty ones, but thanks anyways

It's true for all real numbers but not for complex ones

Complex numbers don't have < or >

Immortal Babun wrote:

vizkosity wrote:why, if not for the fact that it's true for all x, y, z?
the maximum isn't greater than 1/2, and in nowhere there is a complex factor in the simple expression. If it's not true for all x,y,z set that follows the constraint, then how is it wrong if there is only 1 factor of lambda available?

and thanks for the video :[ Although i expected something that is classier
not really a fan of slutty ones, but thanks anyways

It's true for all real numbers but not for complex ones

Complex numbers don't have < or >

i thought we were talking about whatever the factor lambda comes out to be. However, i guess you can project it on a real-imaginary axis, having the magnitude of the whole thing on the real axis....

so in short, e^(ix) based on Euler's formula with x being 0 :/
thus isinx part would be 0 in limited case....

Again, there's no < or > for complex numbers unless you use their norms which isn't the case in this example

Immortal Babun wrote:Again, there's no < or > for complex numbers unless you use their norms which isn't the case in this example

.....

oh well, the only time i will probably ever use complex number is some complex analysis with maybe things like phasors, quantum and AC circuit. Not planning to be a theorist anyways.

like i said, it was a limited case with the whole imaginary axis having 0 magnitude. So in short, it only has real components, hence real numbers

What sort of places hire physicists and mathematicians?

vizkosity wrote:

Immortal Babun wrote:Again, there's no < or > for complex numbers unless you use their norms which isn't the case in this example

.....

oh well, the only time i will probably ever use complex number is some complex analysis with maybe things like phasors, quantum and AC circuit. Not planning to be a theorist anyways.

like i said, it was a limited case with the whole imaginary axis having 0 magnitude. So in short, it only has real components, hence real numbers

The question was whether it's true for all x, y, z

I could give just one example:

Assume (x,y,z) =(1,i,-i) with i²=-1,
then
x+y+z=1+i+(-i)=1 but xy+yz+xz=1i+i*(-i)+1*(-i)=i-i²-i=1 > 1/2

One counter-example is enough to deny the ' true for all' theory

Immortal Babun wrote:

vizkosity wrote:

Immortal Babun wrote:Again, there's no < or > for complex numbers unless you use their norms which isn't the case in this example

.....

oh well, the only time i will probably ever use complex number is some complex analysis with maybe things like phasors, quantum and AC circuit. Not planning to be a theorist anyways.

like i said, it was a limited case with the whole imaginary axis having 0 magnitude. So in short, it only has real components, hence real numbers

The question was whether it's true for all x, y, z

I could give just one example:

Assume (x,y,z) =(1,i,-i) with i²=-1,
then
x+y+z=1+i+(-i)=1 but xy+yz+xz=1i+i*(-i)+1*(-i)=i-i²-i=1 > 1/2

One counter-example is enough to deny the ' true for all' theory

i already admitted that mine only works for limited cases, which happens to be real number. Maybe i speak too much in a physical sense. But yea, we almost never worry about those complex numbers in anyway. They usually don't represent anything, rather than the math, and taking the real part of a complex number will give other things, or the angle theta they project on a complex plane ( things like phasor, AC current in our houses, impedence of a resistor/device, ect...)

In a sense, yes you are right, i did not think about it in a mathematical sense. As a physicist, it's obvious enough that i throw away solutions that don't represent anything interesting for me. Ex, negative time from quadratic equation. It makes no sense whatsoever, since we can't travel faster than speed of light. However, it's part of a mathematical solution in a given quadratic equation

I'm not even close to a pure mathematician But you are right, I neglect the complex possibilities as it makes no real sense for me whatsoever






About the relativity problem, it's not that hard if you can draw 2 diagrams, 1 posing what a moving guy sees, the other one represents what a resting person sees

beatrixasdfghjk. wrote:What sort of places hire physicists and mathematicians?

many places

mathematicians are extremely logical, and smart at what they are doing. They tend to have a very good logic/order/ yet abstract enough to think differently.

Physicists on the other hand, have to learn a lot of math, as well as mathematical physics. We tend to have a logical thinking process that involve the natural world, as well as many applications. Our interest can sometimes expand outside of physics. Although not abstract and formal as a mathematician, a physicist can think reasonably well enough to hold most engineering position (not as polished as engineers though), yet still understand about the physics and properties of what they are dealing with.

about 30% of the physicists also major in math Sadly i don't. I worry too much about my GPA as well as graduate school
Places that would like to consider us are banks, wall street, industry of various positions, government post, school, ect....almost anything that required critical thinking.

most of us don't do pure math or physics once we graduate, either it's BS or phD. Only about 20%? of physicists who graduate get to research and do actual physics.


Not like you will remember what you learn after a few years anyways. I personally plan to go into either semi-conducting businesses, or medical physics just for the money

Bad idea, but i think i will like it

Vizkosity, there's a joke between mathematicians and phycisits

Two mathematicians and two physicists ride a train towards a science summit. Maths guys have one ticket, physicists 2. When the train conductor arrives both mathematicians go into the toilet. The conductor knocks at the door. One of the maths guys slides the ticket underneath the WC door. Physicists think ' those guys are smart'
On the way back from the summit, physicists want to try their luck with the same trick. Maths guys didn't buy a ticket at all this time around. As the conductor arrives both physicits close themselves into the toilet. One of the mathematicians goes to the next toilet and the other one knock on the door where the physicists are

Moral of the story:

Physicists use maths concepts without really understanding the core
( It's a joke, no offence)

There's another one for physicists

A maths and physics professor are asked the following question:

What do you think of the prospect of having a georgeous naked girl on one side and yourself on a stool on the other side? You're only allowed to halve the distance at a time between yourself and the girl.

Answers:

Maths prof: I'd go crazy! I'd never reach her in enternity

Physics prof: after numerous repetitions I think I'll be close enough for all practical applications

^
the 2nd joke is more of an engineering one Physicist would say infinitely, mathematician would say never, and engineering would say after a couple of tries.


But yea, many physicists use the math without fully understanding it. It happens so much in abstract algebra, quantum, as well as other things. However, the solution generally carries out a meaning in a physical sense to us. Everything that doesn't = throw it away. As much as i can say, mathematicians are extremely smart, yet not so practical....and ofc, they take things too formally (ex. physicist would divide by 0 and gives infinity as an answer in no time).


However, many physicists are also mathematicians as well as from other disciplines. Most of the science today are generally credited to physicists (also the reason why i want to be one), ranging from bio to chemistry. Einstein/newton are less of mathematicians, yet they command so much respect, as well as arguably the most influential people of all time beside jesus/other prominent figures.

Moral of the story,
physics is just a branch of mathematics that happen to apply to something. Math is used as a tool to understand the physical concept rather than being treated as what they truly are.

however, mathematicians also make great programmers due to their logical thinking ability (as well as physicists, but informally). Pure math has less emphasize on application, but physics, econ-math, financial math, stats, actuary are all very practical.

anyone solving that problem :[?
It's not hard at all, i swear. Start visualizing lol

vizkosity wrote:while we wait for the answer, or confirmation from you guys, I have an interesting question (if you really like science, you will find this fascinating).

topic: Special Relavity
difficulty: easy
requirements: Know pythagorean theorem, basic algebra, and the fact that speed of light c, is the same for every reference frame.

Prove:
Using the light-clock old fashion lecture, prove that
t' = gamma* t, where t is time clock in the rest frame, and t' is time in the moving frame.

Please explain why is this important to our lives, name the most frequently used electronic that applies special relativity and why would one appreciate it so much

High school math required, no need for derivatives/integration/calculus of any kind. Transformations aren't needed either oh and distance = speed of light * time

Good luck

Winner will get....ummhh...some hot kpop girls D:?

I don't know much about boobslips, ect...
Hint: gamma is always bigger than 1,

You might be interested in this one:
http://milesmathis.com/emc.html

it's called lorentz' transformation and einstein redefined newton's concepts
Yes, i took a course on it, and pretty interesting. It took him 8 years further to prove that gravity also affect time (which is very complicated and i missed the class this year)

here's the solution







i'd be happy to clear up any misconception. As we can see, if we travel a lot less than speed of light, our clock will agree, because gamma will be close to 1. make sense. If we travel close to the speed of light, our clock will tick slower Hence, we age less than ppl who live on earth.

As for its application, the most famous ones are GPS and sattlites. Why is it important? Because if we didn't take special relativity into account. Your car will be hundreds of meters off from its designated location when the signal reaches you

Very easy math, just need to know that the speed of light c is the same for everyone's frame

Gamma is bigger than zero, if we break the speed of light, then our equation breaks down. Same thing when light gets inside a blackhole

excuse my 2nd pic, it should be [delta (t')* v]/ 2, i wrote it wrong :I

genius

Of course the person with an Asian as their d.p. would be insane at maths.

Am I allowed to say that?

plz dont embarrass me, it was just some algebra and imagination (not even my own imagination really...) Einstein came up with it while he was bored with his desk job

Babun

vizkosity wrote:plz dont embarrass me, it was just some algebra and imagination (not even my own imagination really...) Einstein came up with it while he was bored with his desk job

I've got a practical question. Force in mechanics is F= m*a. I want to know how much force is applied in sprints compared to squats, roughly.
My overall guess is that it's a lot greater because during squats you stay in one place druing the contractions and the weight is divided between two legs while during sprints you have to move your body forward from the ground with one leg only with applied acceleration.

P.S. you don't need to be precise. Just give me some scientific explanation in formula ( physics)


Background story:

Sprints kill me off faster than any type of squating

Dolce Vita wrote:

vizkosity wrote:plz dont embarrass me, it was just some algebra and imagination (not even my own imagination really...) Einstein came up with it while he was bored with his desk job

I've got a practical question. Force in mechanics is F= m*a. I want to know how much force is applied in sprints compared to squats, roughly.
My overall guess is that it's a lot greater because during squats you stay in one place druing the contractions and the weight is divided between two legs while during sprints you have to move your body forward from the ground with one leg only with applied acceleration.

P.S. you don't need to be precise. Just give me some scientific explanation in formula ( physics)


Background story:

Sprints kill me off faster than any type of squating

umm....i'm no biologist or physical therapist so i don't exactly know how the human body behaves. However, sprinting and squatting are very different ( i probably dont even need to say this). I play soccer, as well as bodybuilding a little ( buffer than balo, and maybe on Ramos' lvl lol), so i can tell you that both serves different purposes.

When you do Squats, you are exerting more force ( not much, because force is mass times acceleration. Although there are a lot of mass, but you probably squats and accelerate your weight very slowly or else...it wouldn't be doing any good right?), the force is approximately the weight of the whole thing. However, as you've expected, squats require a lot less power (mind you, power is work per second in physics). Let's say the weight is 80kgs and your body is another 80 kgs(1600 Newtons in total because 160 kgs*10, which is the acceleration of gravity) and you squats every 2 seconds, that's exerting a power of 800 watts.


However, when you sprint, you basically raise up your whole body off the ground in less than 0.3 seconds (or else it would be jogging?), so your power is about

bodyweight in kg * 10* distance you jump off the ground by each step (vertical component up and down for the most part)/0.3 = 266 Watts ( if you jump about 0.1 m off the ground).

you can calculate it out.


Mind you, power is NOT the force being exerted, but it's the work/energy spent per second. So in fact, you can squats with a great deal of force, but you take it too slowly...as opposed to sprinting. Also, you can only squats over a short distance (up and down), but you run a lot more than you squat up and down, so it will make up for it. As for why it kills your legs, the answer is probably the amount of work/energy your muscle spent. Force can be part of the equation, but let's face it....you won't get your legs killed if you sprint for 200 meters as opposed to running for 10-15 miles.

It's the same concept, if you squats for 200 meters up and down in less than 0.1 sec each, it will probably kill your legs easier than sprinting

Again, i'm no biologist or physical therapist, but that's my guess

You ignore the horizontal component too much
With each step, one has to absorb ground resistance completely then lounge forward with greater force. Neverthless, all the mass is supported by just one leg during sprints If you regard it this way, a 80kg man supports his 80kg with just one leg. A 80kg man who squats with 80kg on his shoulders supports 80kg with each leg as well. In other words, while you sprint it's like carrying your bodyweight on your shoulders
The acceleration is also much greater during the sprints than a squat I think. In sprints you have to add the vertical and horizontal vector components while during squats you only have the vertical one.
I'd say ,per leg, much more force is produced than with squating=> more hypertrophy.

I'm asking for force because it stimulates hypertrophy in muscles. Leg muscles are more responsive to higher reps than other parts.


If my rough estimation is right a sprinter does more work both in power and volume ( reps) than a squater with his bodyweight on his shoulders in 5 sprints/ sets.

Dolce Vita wrote:You ignore the horizontal component too much
With each step, one has to absorb ground resistance completely then lounge forward with greater force. Neverthless, all the mass is supported by just one leg during sprints If you regard it this way, a 80kg man supports his 80kg with just one leg. A 80kg man who squats with 80kg on his shoulders supports 80kg with each leg as well. In other words, while you sprint it's like carrying your bodyweight on your shoulders
The acceleration is also much greater during the sprints than a squat I think. In sprints you have to add the vertical and horizontal vector components while during squats you only have the vertical one.
I'd say ,per leg, much more force is produced than with squating=> more hypertrophy.

I'm asking for force because it stimulates hypertrophy in muscles. Leg muscles are more responsive to higher reps than other parts.


If my rough estimation is right a sprinter does more work both in power and volume ( reps) than a squater with his bodyweight on his shoulders in 5 sprints/ sets.

sprinting causes a higher power because its a very short blow of energy where you use both adrenaline and ATP energy, these 2 components allow your body to achieve extremely high work for a very short amount of time.

i recently watched a show on the discovery channel on sprinting and they showed that a 100m sprinter will achieve his top speed before 55 meters and from that point on he will actually decelerate as he has used up all his ATP energy. The show also showed a fireman who was escaping a burning building about to explode, when running away for the house he actually ran as fast as a professional sprinter for a few seconds. interesting stuff..

also when sprinting there is a totally different stress tensor as you are pushing the surface behind you, so u are in fact getting shear stresses, whereas during squatting you get mostly normal stresses and some shear stresses.

spanky489 wrote:

Dolce Vita wrote:You ignore the horizontal component too much
With each step, one has to absorb ground resistance completely then lounge forward with greater force. Neverthless, all the mass is supported by just one leg during sprints If you regard it this way, a 80kg man supports his 80kg with just one leg. A 80kg man who squats with 80kg on his shoulders supports 80kg with each leg as well. In other words, while you sprint it's like carrying your bodyweight on your shoulders
The acceleration is also much greater during the sprints than a squat I think. In sprints you have to add the vertical and horizontal vector components while during squats you only have the vertical one.
I'd say ,per leg, much more force is produced than with squating=> more hypertrophy.

I'm asking for force because it stimulates hypertrophy in muscles. Leg muscles are more responsive to higher reps than other parts.


If my rough estimation is right a sprinter does more work both in power and volume ( reps) than a squater with his bodyweight on his shoulders in 5 sprints/ sets.

sprinting causes a higher power because its a very short blow of energy where you use both adrenaline and ATP energy, these 2 components allow your body to achieve extremely high work for a very short amount of time.

i recently watched a show on the discovery channel on sprinting and they showed that a 100m sprinter will achieve his top speed before 55 meters and from that point on he will actually decelerate as he has used up all his ATP energy. The show also showed a fireman who was escaping a burning building about to explode, when running away for the house he actually ran as fast as a professional sprinter for a few seconds. interesting stuff..

also when sprinting there is a totally different stress tensor as you are pushing the surface behind you, so u are in fact getting shear stresses, whereas during squatting you get mostly normal stresses and some shear stresses.

My sprints are about 60m long
If you have a link to the show let me know. I'm very interested
From muscle hypertrophy point of view sprinting is a very fast explosive movement where muscle fibers contract in quick succession. If we follow the theory then the target would be fast twitch muscles type 2b. It's equivalent to maximal strength training in bodybuilding. People wouldn't bulk up from it much. Bodybuilders usually target slow twitch or intermediate muscles with 8-12 rep range. If that's true squating in 2-5 rep range would make one a faster sprinter :I'munoriginal:

i have no video, that was just purely my speculation. However, sprinting isn't an endurance exercise either. It's more of a HIIT workout, and your body can use a bunch of power during those excercises. Your heart rate is the result of such thing, but as i stated, it takes more than just mechanics to figure out why.

Sprinting definitely make you work more than however much squats would, just because of the distance ur body moves, as opposed to someone squatting like 1000 times to match the distance. Plus, sprinting drains your glucose more than burning fat, since it's HIIT.

http://forum.bodybuilding.com/showthread.php?t=108975221&page=1

may shed some light

Squating can make you stronger, but not neccessarily faster. Sprinters tend to lose a lot of more weight from fat, ect...while squating can increase your power. Wingers and fullbacks in football can be extremely skinny, yet quick. But anyhow, squating will give you better power and thus, sprint faster providing both have the same mass/endurance

vizkosity wrote:i have no video, that was just purely my speculation. However, sprinting isn't an endurance exercise either. It's more of a HIIT workout, and your body can use a bunch of power during those excercises. Your heart rate is the result of such thing, but as i stated, it takes more than just mechanics to figure out why.

I never mentionted sprinting with cardio

vizkosity wrote:
Sprinting definitely make you work more than however much squats would, just because of the distance ur body moves, as opposed to someone squatting like 1000 times to match the distance. Plus, sprinting drains your glucose more than burning fat, since it's HIIT.

It burns more sugar than fat at first but at the same time hormones are released which signal to the body to use carbs sparely which makes fat metabolism faster.
It's the best way to lose fat, not just 'weight'

vizkosity wrote:

http://forum.bodybuilding.com/showthread.php?t=108975221&page=1

may shed some light

They missed the crucial part which is genetical predesposition. They conclude that sprinters who squat ridiculious weights are faster because of squats I was able to squat 80kg easily in my first week of weight training Some other people had ridiculious chest strength in bench press ( my weakness).
I'd say max squat strength is an indication of how fast one could run, not the factor which enhances it the most. Of course, if the legs are underdeveloped squating might help reach top speed faster.

vizkosity wrote:
Squating can make you stronger, but not neccessarily faster. Sprinters tend to lose a lot of more weight from fat, ect...while squating can increase your power. Wingers and fullbacks in football can be extremely skinny, yet quick. But anyhow, squating will give you better power and thus, sprint faster providing both have the same mass/endurance

In professional sports, performances is understood differently from bodybuilding where max hypertrophy is the best result. If your skinny footballer squats more than 2x of their weight they're clearly above average no matter how small or big they're.