Oh boy. And then that means that if m is in any way a positive number, as in one hydrogen atom, then the e is almost infinity squared . That is the atom bomb.There it is-- nuclear power.
Yeah. So before going to improvisation, I like you introduce you one man, my mentor. Squared 2 is something like that, which is often used in the in many mysterious movies
Then the other thing is the physics. Again, very basic, but you said E equals MC squared a couple times. Can you explain this equation? - E=MC squared is a fundamental relationship that a patent clerk, Einstein, discovered and unlocked an entire new realm of physics and engineering and has shown us engineering and has shown us atomic physics, what happens inside the nucleus, and unlocked our understanding of the universe and paved the way for many of the physics advancements that came after.
you find out instead of expressing 48 chains, they only express 24. Del squared psi plus V times psi equals-- it can be anything.
you find out instead of expressing 48 chains, they only express 24. Del squared psi, we know how to compute.
So 1 squared is 1. 2 squared is 2 plus 2. 3 squared is 3 plus 3 plus 3.
2 squared is 2 plus 2. 3 squared is 3 plus 3 plus 3. And 4 squared is 4 plus 4 plus 4 plus 4.
Yeah. 1 is 1 squared . 1 squared plus 1 squared . But 3 cannot be expressed like that.
But pi is 1 plus 4. 1 squared plus 2 squared . Are you following me?
And so the second section is from-- I think I set it in '83. I squared my shoulders and made my entrance, walked solemnly to the lectern on the podium.
And Diophantus talked about the fact that there are lots of solutions to the Pythagorean equation, x squared plus y squared equals z squared . 3 squared plus 4 squared equals 5 squared . 5 squared plus 12 squared equals 13 squared .
3 squared plus 4 squared equals 5 squared . 5 squared plus 12 squared equals 13 squared . There are lots of solutions to that equation.
So we'll start off with clothing. I squared up to it, yelled at it.
So if you've got a cross-sectional area of two centimeters squared for the main vessel, then each of the two branches need to have an area of one centimeter squared each, for large vessels at least. For smaller ones, daughter branches can be a bit thicker to allow blood to slow down and exchange resources with the tissue it's reaching.
- As a result, the Hausdorff dimension of the surface of the circulatory system is roughly three, meaning its surface area doesn't scale as its length squared , but it's length cubed. And since the metabolic rate hinges on how fast resources can be exchanged across the surface area, well, it must also scale like length cubed.
In other words, he found that energy must be equal to mc squared . E equals mc squared . - Mass and energy are but different manifestations of the same thing.
Well, think of a very simple second-order time derivative. Something like d squared y over dt squared is equal to 3. Now, to figure out what y is, the function that satisfies this equation, we just have to integrate it twice.
These terms do match on both sides, which tells us that alpha x squared must be equal to 1, and so must alpha y squared , alpha z squared , and beta squared . So Dirac now had a set of simultaneous equations for alpha x, alpha y, alpha z, and beta that he just needed to solve. That sounds easy, right?
Now, I know that, depending on your physics background, you probably think you've heard of Einstein's equation. E equals mc squared is extremely famous, maybe the most famous equation in physics. But this is not what professional physicists refer to as Einstein's equation.
That's what capital G is, just a constant everywhere in the universe, times the mass of the object doing the pulling divided by the distance to that object squared . And what you notice is the actual mass of the thing falling appears nowhere in this equation.
You wrote down some axioms, and then you proved some theorems. say interval squared , either spatial interval or time interval, is some number of times t squared plus some number times t times x
You wrote down some axioms, and then you proved some theorems. coefficient of t squared , tx, et cetera.
You wrote down some axioms, and then you proved some theorems. G00 times x0 squared plus g01 times x0 x1, g02 x0 x2, all the way through the 16 combinations.
You wrote down some axioms, and then you proved some theorems. Here's t squared . Gtt, which is the coefficient there, is telling you the relationship between the time you experience and the time coordinate
You wrote down some axioms, and then you proved some theorems. E equals mc squared implies that mass is a form of energy.
I don't need to know the circumference. e equals mc squared , I don't need to know that or whatever. So I think that I was OK with just like getting a 70 and just passing.
So our brain's far more like the battery on our phone than we let ourselves believe. But how have you squared thinking about client meetings versus other meetings?
The distribution of collagen is changing, the health of the skin is improving, the density of facial hair is going down. This is r squared .
And the answer is about 25%. This is an r-squared form of regression, for those of you who remember, . So in other words, these company accounts here-- very uninformative about the set of assets which are really powering a company.
equals mc squared with similar logic.
If you have that squared away, then everything will fit into that framework.
pi r squared . pi r squared ?
You may know you can have a 3, 4, 5, right triangle. That means 3 squared plus 4 squared equals 5 squared . So two squares can add up to a square .
We're dealing with squares, we need two dimensions. So 1 squared is 1. 2 squared is 2 plus 2.
3 squared is 3 plus 3 plus 3. And 4 squared is 4 plus 4 plus 4 plus 4. So let's take our sum and make those substitutions going down.
Do the same idea and you can eventually with a lot of work show that the sum of the first n cubes is n squared times n plus 1 squared over 4. It's not easy. I'll give you a little more homework, which is much more interesting.
And that's good enough. It is pi squared over 6.
rather than A squared plus B squared equals C squared .
It's squared .
an awful lot of squared paper and an awful lot of patience.
Our A-squared is Animal Awareness.
The third trigonometric function squared .
is a squared plus b squared equals c squared .
Or x squared plus y squared plus z squared is a constant square of the radius.
get this squared away so they went to the diocese and they ask the bishop for
That's of course 1/2 mv squared .
If you take its modulus squared , you get the probability density of finding a particle at a given point, at a given time.
Because the integral is 5x squared plus.
That's because volume is proportional to radius cubed. But surface area only grows as radius squared . So the elephant's surface area only increases by a factor of 100.
Now, we can rewrite this to see how metabolic rate scales as a function of mass. Surface area is proportional to radius squared , so we can swap that in, and if mass is proportional to radius cubed, then radius must be proportional to mass to the one-third. Plugging that in for R, we find that metabolic rate should scale with mass to the two-thirds.