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.
Congratulations for being so practical. This reminds me of the historic story when Edison was manufacturing light bulbs and for some reason he wanted to calculate the volume of the complex shape of a glass light bulb. Apparantly the mathematicians came up with some approximations but were not so sure about the accuracy of their result. Then Edison who was a very practical man came along and filled one glass bulb with water and he knew the volume of the water and also floated or immersed the glass bulb in water thus displacing the water according to Archemedes principle and again he found the outside volume of the bulb , hence he could find the volume of the glass used in the bulb. Mathematiics are very useful but being practical sometimes gets quicker results.
Edison was on a camping trip in 1887 near Rawlings Wyoming, Battle Lake when he dropped the tip of his bamboo fishing pole in the cap finite noticing the glowing car nixed fishing pole tip.... I've driven by the spit many times it is marked with a historical marker. Story is a bit iffy but makes for a good tail.. That's why I go fishing, to be inspired to invent the next big thing, my story to my wife and I'm sticking to it...! 😊
+EscapeMCP This was a huge cube. 20 resistors across at least. So a facing side was a 20x20 array. The idea was to guess resistance from corner to the opposite corner across the cube. (min path=3 in your example) Some one had donated a thousands of preformed 1K resistors I kept growing it until my soldering hand got tired.
Effective resistance across the single resistor is 2R/M. M is the number of resistors (R) connecting to each junction. For your square mesh M=4. If the 2D mesh was actually a 3D cube, then M=6
I'm going to build this at this year's Mini Maker Faire in Honolulu. I already bought 500 10K 1/4-watt metal film 1-percent resistors. It'll be interesting to see how many people will actually stop by and ask what the heck I'm doing. Have soldering iron, will travel...
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.
Hi Dave, This is fantastic (along with all your other videos). I like your comment about practicality and actually doing something as opposed to endless calculations. Cheers, Greg.
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: 12x12, then 10x10, etc. Or if I get around to build one, maybe take measurements as it is being put together.
David Scott Any finitely sized network has resistances that are a truncated sum of an infinite series. It’s possible to prove that by induction. The convergence rates depend, among other things, on how many dimensions does the resistor grid have. Try going from a 2D grid to a 3D grid with roughly same number of resistors. Then a 4D grid. Then try going from a hyper cube (square, cube, …) to hyper sphere shape (circle, sphere, …). You’ll get quite a tour of various forms of infinite series, and can then ponder questions such as “does the circular grid converge similarly like a square grid would”. While doing so you’ll rediscover some cool theorems in calculus. All from a “simple” resistor network. I urge anyone who’s so inclined to try it out. Sometimes having a physical object to think about makes the math easier to understand. That’s certainly the case for me. When I took a mechanical vibrations course, in my mind I modeled everything with electrical circuits :)
My own thought too. A geometric toroid. Intuitively i would think it would - then you could shrink that down to just a few resistors and solve it theoretically too.
Seeing you love measuring stuff, how about applying a voltage (say 10.000V) to the central resistor, and then measuring the voltage at various locations around the grid.
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 really glad I saw this.Brilliant. I also agree with crapcbm, a circle would be great. I'd do it if I had a big box o" resistors laying around. Cheers
That Infinite Resistor Network you built is almost close enough to keep Rhode Island mosquitoes out. And... 420 of them to make up a problem that could keep a stoned engineer busy for hours!
That reminds me of going to school . The teacher drew up a 3 D cube of 100 ohm resistors , and said that anyone in the class who could solve it , would get an " A " grade . I didn't build the thing , I just did the math ! and got an " A " grade in the class ! anyway , Cheers , take care , and have a good day !...73 Ray aka KE8CWT & PG1920311
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.
Really good work mate. nice to see some fellow aussies getting themselves out there. love hearing measurements in millimeters and grams saves having to try and guess the values the yanks are talking about all the time. What company are you working at currently?
Dave I am a brazilian physics teacher. In Brazil most of people do not speak English. Would you mind if I use just a single of this video, around 3 minutes of it, translate your voice comments into portuguese to present it to my pupils ? I used my own voice in portuguese. Do you authorize me to use a peace of this video with this little changes ? In the end of the video, I gave all the credits to you, to your excelente Blog, I showed the URL of you blog here in RU-vid.
I prefer less math and more practical things too :) I was thinking if anyone build it and how large and then you showed it, pretty nice :) The measurement is close enough, you don't need like 5 digits for most things anyway
The math is very nifty though, and it’s not much more than good high school level math. It’s really cool how far simple math can go in modeling fairly complex physically realizable structures.
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?
Haha :D ..thank you Dave! (..just watching this video now, and just 'had' to stop at plbckPos 3m20sec and coment it. Starting to watch again the rest.. )
Why not connect the ends of each row and column, such that electrically there would be no center. Each resistor would be attached to the same number of resistors in every direction, kind of like a scrolling game. Would this work?
I wonder if this is the kind of problem/solution one would find while measuring the resistance on 2 points in a flat conductor. I've thought the closest thing to an infinite grid in real world would be a grid along the surface of a sphere. What do you think?
I think the topological equivalent of the infinite grid would be a torus rather than a cube. Anyway, when you measure the resistance, that topology changes again so that there are also infinite zero-resistance "connections" between points at equal distances in the equivalent infinite grid.
+orbik Nicely said. If a grid of perfect zero tolerance resistors were overlayed on a toroid, would the measurement on any resistor or diagonal measurement (as dave did on 2D sheet he made) remain constant anywhere measured on the toroid? I expect it does. But can we apply a constant knowing how many resistors are in the grid and still get daves formula ?
unlost117 I think that depending on the size, it will show an not perfect value, but it will show the same error value no matter where you measure. :-)
It doesn't work. If you think of a torus of only a small number of resistors (say 9 or perhaps less), it quickly becomes clear you can't make resistors apply multiple times in a way that makes it look like an infinite grid.
Actually, you can build an icosahedron or any other platonic solid as an approximation of a globe. Such networks have an interesting duality property, see ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-PfIsWtXWNX4.html. This property was found by my student Martina Furrer and was later generalized in a joint paper with Norbert Hungerbühler and Simon Jantschgi: arxiv.org/pdf/1805.01380.pdf And one can of course also verify the duality theorem experimentally, as done in hsr.othello.ch/duality.pdf (in german, but see page 7).
365 resistors..... I'd rather do the math By the way I am reading your "PCB Design Tutorial" which is simply brilliant put it on the tube mate it will be useful to a lot of people on the tube
My friend and I are going to totally make an infinite resistor grid out of 0Ω resistors for the lulz. It'll make a cool necklace and stump people :) (EEV isn't supposed to be -VEE backwards, is it? :P)
Nova Fawks PI usually a comes into play in discrete systems when some quantity is effectively a sum of an infinite series (or a nested fraction). PI appears in sums or limits of quite a few series.
Sorry bout the rant. I was on Facebook typing to my friends just a bit earlier and we were dissing guitarists. (I am one) We let it get a bit out of hand and I had to leak it instead of shunting it. Peace be with you my siblings in internet fun. the rugburnz 😰
Write out formulas for progressively larger networks, and you’ll see that the resistance is a sum of an infinite series. And the infinite series happens to be the one whose sum is some constant times the reciprocal of pi. Ou arises in many infinite series sums with nested fractions. Conversely, you could ask how to calculate pi using nothing but a 4-function calculator. This resistor network is a physical model for that :)
Nothing\ The analysis of any particular size of it is instructive, but it gets even more instructive when you see the patterns that are a series sum, and then you can get an analytic answer for an infinite grid without building one - and you can inductively prove that the answer you get indeed represents the result for an infinite grid.
i dont think thats the same. you would simply measure the resistance between the two probes, without taking parallel paths into account. just a guess tho
that would only be a 40 cm by 40 cm square, neglecting connecting traces. thats a pretty big pcb, but lets do a 10x10 of those squares and get 100 million lol
Wouldn't you expect the tolerance to increase over the total number of resistors? If the tolerance is 1% per resistor you are using, it would be 5% if using 5 resistors?
Not necessarily, actual tolerance calculations are more complicated, but just look it this way, if you have 1% 1ohm resistors, you expect them to be within 0.99 and 1.01ohm. If you use five of them in series, your expected result would be within 4.95 and 5.05ohm, which is still 5ohm 1% tolerance
i created a series of videos on that topic: ru-vid.com/group/PLoGRr8ff1uXESrWh6z0BNTYpc4Y-hlBOm starting with EE basics. at the end also some numeric simulation with numpy.
fun fun fun. However, approach infinity at your peril ! infinity is not a number is it aka + fun - fun + fun - fun... is it. + ( fund fun+ fun ) or -(-fun +fun -fun). ! ! ! ! IDK 1fun+2fun+3fun+4fun... = -1/12 fun = LESS THAN NO FUN @ ALL. math is easy. engineering is hard! AKA @ the end of the day something needs to get built. AKA when the arrogant lead guitarist's $13000 hand soldered by children paid $7.89 per day tag board tube amp doesn't work it is YOUR FAULT. It is NOT at all the sales rep's that told him UNDERATED output transformers and 25watt super Distortionated double doped SELLestions are conservatively rated! "Make it work nerd!" is his polite response. OH SH!T I IS ON A RANT I'll stop sorry.
