The infinite resistor grids (in 2D, 3D, 4D, …) are awesome to demonstrate how physical structures give rise to sums of infinite series. Conversely, as a rule of thumb, if you have a series and can think of a resistor network where resistance between some two nodes is a sum of the series, then the series converges. This can actually be mathematically proven, no less.
In the early 80's there was an article about an artist who did 3D sculptures made of components. They were real circuits. One of them detected someone passing by and made strange noises that varied with their position and speed.
I know this video is old, but I just recently found your channel. Amazing that the result is 2/pi. I like your practical approach. Would be interesting to see how the result changes if you gradually chop it down to smaller networks: 12×12, then 10×10, etc. Or if I get around to build one, maybe take measurements as it is being put together.
As people have asked about three dimensional versions of this it occurs to me that if the lead lengths were constant, the resistance value between any two points might well be a constant percentage of the value of one resister. I initially expected the diagonal value to be 1/2 of the square root of 2 or .7, which it is nearly is. If lead lengths are all the same, then we can probably model this as a solid block of conductive material.
I'm always curious what causes people to give a thumbs down to a video like this. I suppose the end of the bell curve needs data, and perhaps it's best not looked at too closely.
This was a great demo.
Question is asked, the person opens up a briefcase and pulls out the resistor network and a multimeter…
It would be really interesting to see reading as the grib was being built to show the convergence of the solution as every new row/column is added
But your expeimental method soes not give you the theory behind the mechanics of the problem… Though I like your arts skills!
please revisit the topic after so many years of youtube!
Hello from the future xD
Array For Dave!!
And now it's time for Big Clive's Resistor Roulette…
#420
You can tell you're not s mathematician. If you were you'd have made a 3D representation of a 4 dimensional resistor network!
The infinite resistor grids (in 2D, 3D, 4D, …) are awesome to demonstrate how physical structures give rise to sums of infinite series. Conversely, as a rule of thumb, if you have a series and can think of a resistor network where resistance between some two nodes is a sum of the series, then the series converges. This can actually be mathematically proven, no less.
How sturdy is that grid? If you want to keep it for decoration, maybe you can also use it to hang other components onto to add a bit of variation.
How about if the outer most resistors on the perimeter were 5K to 'terminate' the grid since that's what the expected resistance would be.
Forget math!
Build bigger resistor array!
Would be interesting to make cylinder or globe 🙂
what about a spherical infinite resistor dave?
I'm new to EE so I'm confused. How does pi come in to play with 2 of them?
It is irresistible 🙂
Good. Now let's analyze the whole circuit if you put 5v on one corner and ground the other. Every single junction for current and voltage drop.
In the early 80's there was an article about an artist who did 3D sculptures made of components. They were real circuits. One of them detected someone passing by and made strange noises that varied with their position and speed.
I'm your host, Dave fucking Jones.
Would the ACTUAL formula for calculating the opposite node of a grid this be:
n / (π * R * (n – 1))
Where n = Number of dimensions, and R = resistance of resistors?
I know this video is old, but I just recently found your channel. Amazing that the result is 2/pi. I like your practical approach. Would be interesting to see how the result changes if you gradually chop it down to smaller networks: 12×12, then 10×10, etc. Or if I get around to build one, maybe take measurements as it is being put together.
As people have asked about three dimensional versions of this it occurs to me that if the lead lengths were constant, the resistance value between any two points might well be a constant percentage of the value of one resister. I initially expected the diagonal value to be 1/2 of the square root of 2 or .7, which it is nearly is. If lead lengths are all the same, then we can probably model this as a solid block of conductive material.
I'm always curious what causes people to give a thumbs down to a video like this. I suppose the end of the bell curve needs data, and perhaps it's best not looked at too closely.
87th!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!