Other than its maths why does it intuitively work.It seems such a weird way of deriving F=ma (from the langrange).Furthermore it seems this was just someone throwing formulas and seeing what came back from it.Damnt Euler was a genius.
Other than its maths why does it intuitively work.It seems such a weird way of deriving F=ma (from the langrange).Furthermore it seems this was just someone throwing formulas and seeing what came back from it.Damnt Euler was a genius.
That's what I'm asking people to explain to me.The best way I can explain it without intense maths is that say you have a quantity S which is action.Now assume you have a "path" throughout that path you have certain relations.Or basically at a point you have a certain amount of energy, certain amount of difference in energy, certain amount of some property.Now the if you add up all the relations in the path , so at 1 you have 5, at 2 you have 6.Now sum them all up with respect to some axis(time, etc doesn't matter).Finally take a path which is the absolute minimum of that action.That path is always preferred.Can u explain in laymen terms? how is it applied
I don't see maths as a language as that implies its singular, rather think of our maths as being a language.Maths itself could have used completely different symbols but essentially if you can translate one maths to another maths it is consistent. Mathemetics has certain axioms which for some reason describe the universe beautifully.Albeit someone without a maths language as no hope of understanding the universe.maths is the most efficient way into understanding the universe , however it seems the universe is limited.Maths goes on to infinity , pure maths comes into play here.Much of the notation used by mathematicians today - including e, i, f(x), ∑, and the use of a, b and c as constants and x, y and z as unknowns - was either created, popularized or standardized by Euler. His efforts to standardize these and other symbols (including π and the trigonometric functions) helped to internationalize mathematics and to encourage collaboration on problems.
This makes sense. He set up a syntax rule that anyone can understand. Constant numbers like the measurement of a certain distance, time, shape, angle, circumference, things u have a definite number for after measuring it. Then the unknowns with a certain syntax the things u wanna find out based on your measurements or what your applying the maths too like taking a leaf shape and applying it to a garden. The unknown is the garden, the leaf can be measured unless there is some unknown in there somewhere. But it breaks ur problem down into unknowns and knowns really.
I simply skip this part when really doing the maths but if I need help on it I will definitely use it so it brings colloboration on the problem from others.
Mind you that is not solving anything the syntax. It's just presenting the problem into a language people can understand, it isn't going to magically give u an answer to your problem but sets your problem into an algorithm that people can understand, this is where I respectfully disagree with @Naissur
Syntax I think he thinks will give him an answer, trust me real maths is 'paper loads' of figures and confusion untill it's simplified into a nice equation or answer. Real maths isn't sitting there and looking at the problem and deciding what is known figures and unknown figures and assigning it the right letter. Come on god dammit, @Naissur I really thought u were better then this. Me and u can figure out what is known and unknown in a leaf and garden pretty quickly and assign letters cause we know what we wanna 'do' which is translate the leaf design into the garden size. We know the garden size and leaf size are different. So an unknown clearly is adjusting leaf measurements to the garden itself. Other unknowns can be accurately measuring the curve on the leaf, and measuring the different points of the leaf cuz it gets smaller and bigger in different areas, the over-all space within the leaf. U can look at what's stopping u from achieving ur goal of making the garden into a leaf in 5 minutes and probably another 5 minutes breaking into the unknowns and known language of algebra.
I am disgusted with my brother @Naissur and refused to respond to him in the science thread.
I don't see maths as a language as that implies its singular, rather think of our maths as being a language.Maths itself could have used completely different symbols but essentially if you can translate one maths to another maths it is consistent. Mathemetics has certain axioms which for some reason describe the universe beautifully.Albeit someone without a maths language as no hope of understanding the universe.maths is the most efficient way into understanding the universe , however it seems the universe is limited.Maths goes on to infinity , pure maths comes into play here.
Numbers going to infinity mean nothing.Its just our curiousity manifesting into an extremity.Well we agree at least numbers go into infinity either direction up and big like the universe and into small grains of a beach sand. U agree the numbers are going into infinity either direction, I hope? plus do we agree any maths or problem will use arimethic functions addition/multiplication/division/substraction to find the answers? Do we accept those arithmetic functions are we are going to use for any problem?
Numbers going to infinity mean nothing.Its just our curiousity manifesting into an extremity.
Nothing special about arithmetic properties they are like commas, fullstops etc.The more advanced our mathematical skils the more operators we have.Calculus was the invention of more operators.This is why it propelled society into a new golden age of physics/mathematics.
Find Feynman's lectures on physics. He gives a very nice explanation. But in general, it's not very intuitive result (though of course beautiful)! Also, always keep in mind John Vaughn Newman's remark: "In mathematics you don't understand things. You just get used to them."Other than its maths why does it intuitively work.It seems such a weird way of deriving F=ma (from the langrange).Furthermore it seems this was just someone throwing formulas and seeing what came back from it.Damnt Euler was a genius.
Obviously I don't have the context, but isn't this from when they are finding the minimum?why is dT/dx = 0?
Isn't this bit of an overreaction, brother? I enjoyed reading that thread, and didn't mean to cause any 'disgust'.I am disgusted with my brother @Naissur and refused to respond to him in the science thread.
Are they on youtube?Find Feynman's lectures on physics. He gives a very nice explanation. But in general, it's not very intuitive result (though of course beautiful)! Also, always keep in mind John Vaughn Newman's remark: "In mathematics you don't understand things. You just get used to them."
Obviously I don't have the context, but isn't this from when they are finding the minimum?
If so the derivative isn't equal to zero; rather, they set it equal to zero to find the minimum.