Making a physical Lissajous curve 

Look, Parker square ain't gonna die. This is Parker Lissajous. Resistance is futile.

"I've done mine in... Excel." Of course you did.

"I'm gonna call this..." Digging your own grave, Parker... Parker Lissajous

The comments section is *exactly* what I expected. #ParkerLissajous

Ah yes, the Parker Lissajous!

"3, that's good enough for π" - an engineer-minded mathematician

"I'm gonna call this..." Oh why are you so eager to have your day ruined?

Last weekend I went to Tompkin’s Square Park, the squarest park in New York. As much as people kid about the Parker Square, it’s truly an example of someone who keeps trying in an imperfect world. Thanks for showing the grit and not just perfection

Your really excelled in this video

The speed ratio of your turntables seems to be approximately 55 to 32 or ~1.72 (as counted via the number of frames one half-turn takes in the sped-up clip at 5:29, assuming equal diameters of the turn tables)

"Near-missajous" is pretty good. Sadly better than the obvious "Parkerjous".

"I could have used this program specifically designed for making pretty math things, but I chose Excel because of course I did!"

Clearly this is a Parker Curve

Classic parker curve

I noticed that your excel demo had shapes that were too far to the left, indicating a likely mistake in the formulas. So i decided to do my own math and found one. Gamma should be: =ACOS(SQRT((G10-E10)^2+(F10-D10)^2)/$H$2) (there was an extra *2 in there) After that fix i tried to recreate your lissajous. i estimated every value needed: A-x = A-y = B-y = 0, B-x = 5, A-r = B-r = 1, speed = 2, stick length = 3.5, offset = 0. The result was surprisingly similar to the one drawn

I'm surprised you didn't try setting them to a "1 to 1" ratio to see what kind of circle-ish thing that would surface.

"Three: good enough for pi." -Matt Parker 2018

Matt, please stay imperfect. Be our Parker Matt. Someone who is right, but not quite right.

I'm going to school for instrumentation. and i was messing around with a signal generator and oscilloscope along with some other electronic components and i saw these curves show up occasionally.. pretty cool to see a video about them i didn't know if they had a name

In the 11th grade, I got access to a pair of tone generators and an analog oscilloscope. I figured out how to set the thing up in parametric mode and I spent hours looking at these things. They're great fun.

Would be interesting to see a 3D version of these curves. Could we express in a math equation any knot? Some knots resemble each other

That explosive ending was one of the best subscription requests I've seen lately

Just waiting for Mr Segerman to build a 4D version.

Parker Curve

You're really great at creating things that are close but not quite right.

6:15 Personally, I'd have gone with "More-or-less-ajous".

I think you could get an honest lissajou curve if you had the rods connected to the turntables through slots, and if you had a way to hold the rods orthogonal to each other.

awesome!

What you have built here, at least according to Wikipedia (which is always right about everything, ever) is a Pintograph, which is a type of Harmonograph. The way most people do this is to use two pendelums. With a pendelum, you can easily restrict the axis of motion for each wave generator to one direction, and more precisely position them. On the other hand, they don't keep a constant amplitude. I'm going to call your invention the Parker Pintograph.

Hey man, Just finished your book. when I read the bit about the domino computer I said to myself "I remember that from somewhere" and then I checked your face at the back of the book and there you were. Thanks for the awesome content and reads.

loving the quote "where, where have I seen that before". So to the moving midpoint pattern, I know not really part of the video, but , to quote a famous mathematician "where, where have I seen that before", I realized it is the Mandelbrot cardioid and as you increased the speed by one you got the next shape( the kidney one) and so forth .

Very nice physical project. Great to see mathematics like this.

What a lovely Parker curve machine!

Fascinating. Loved it. Didn't understand a word of it!

back in highschool (we're talking end of the '90s) I programmed in qbasic a little thingy that, given the two relative frequencies of the x and y components, plotted the lissajoux figures with slowly increasing offsets, and after that it projected on screen the figures in an animation-like sequence. It was quite beautiful as you could visualize it as a single string around a spinning invisible cylinder, and I was very proud of my work. I think I also got highest marks in programming for that little creature :)

I love how the green shape in the middle of your program sheet resembles cardioid. :)

It's pretty cool that it kind of graphs a surface.

Geogebra is such a great piece of software. Even for more mundane tasks. It's so easy to do geometry tasks with it.

That is some spicy excel work

THAT IS AWESOME! What a great use of Excel! AAAAA! I want to see ratios with various irrational numbers.

Ah! Finally a video about the Parkerjous figures!

I love when Excel is brought out. It's like math that you can while you're running reports.

Near-missjous. Give this man an award.

In fact, when I was very young, like in the 70s, I had a subscription to a magazine called De Jonge Onderzoeker (the young researcher) and there was an article in it with a sort of pendulum. It had a fixed length in one direction but you could alter the length in which it moved in the direction perpendicular to that. At the bottom of it was a small flask with sand, a little hole that let the sand seep through. It made perfect Lissajous figures!

I love the theme song for Stand-up Maths. On a slightly different note: when you comissioned it, did you specifically ask the composer to make it end unsatisfactorily? Did you ask them: make it unresolved at the end, I want people to feel like something is missing, and keep waiting for it, and for it to never come? Is that how this theme was conceived? Honestly, I do love it, really.

You guys are all joking about Parker Lissajous but idk nearmissajous is a pretty fine name to me :p That Excel plot, on the other hand... I think we can safely call that a Parker Nearmissajous?

Really cool video!

I have absolutely no idea what is going on here, but it looks fun.

I remember a program to draw Lissajous curves on a BBC Basic computer, long before I knew even what trigonometry was, let alone parametric curves. No idea how it worked, but it did draw pretty patterns!

This is fascinating.

Aha ha...So,What's going on? So cute! Awesome presentation! Congratulations!

Matt, this is bread and butter undergrad Kinematics stuff for Mechanical Engineers. Look up +"5-bar linkages" +"2 degrees of freedom". That's what you have synthesized. Now if only I could magically remember everything I learned in Differential Equations... then I'd be somewhere.

Pulling out weird "art" supplies, I felt like I was watching Jazza for a second.

Not going for #parkerjou?

That missajou pattern was cool. Like modern architecture drawing. Or like some of those thermodynamic graphs that have way too many variables in the same picture. Was actually a bigger fan of the midpoint patterns than the actual drawings.

And this is why mathematicians don't build things in the real world.

So now you’ve made an Excel Spirograph. Love it! What other classic toys can you recreate in Excel?

Excellent Parker Lissajous ;)

Proper plotter's that did the same line going forward and backwards were robust machines. The pens were as short as possible and the moving arms were anchored at both ends. About the parametric equations: One get very nice polynomials out of one of those. This is how I've described it previously: Here's one each order starting from 1, which is y = x, the order two one is y = x^2 - 2, the third order one is y = x^3 - 3x, the fourth order one is y = x^4 - 4x^2 + 2, the fifth order one is y = x^5 - 5x^3 + 5x, the sixth one is y = x^6 - 6x^4 + 9x^2 - 2, etc. These are polynomial functions that have the following properties: 1. All local maxima and minima values for y are 2 or -2 and their corresponding x-values are between -2 and 2. 2. Each odd function goes through points (-2, -2) and (2, 2) and even function through (-2, 2) and (2, 2). These two properties mean that the polynomial oscilates between -2 and 2 when x goes from -2 and 2. Outside the range the function goes monotoniously to (minus) infinity. 3. The coefficients of the polynoms are integers and the leading coefficient is 1. This is something I find beautiful. That there are integer coefficient polynomials with leading coefficient 1 that have all zeroes inside small range (-2, 2) and that at the same region the polynomial function don't exceed -2 or 2. They can be generated by the parametric pair x = 2cos(t), y = 2cos(nt), where n is the order of the polynomial. The pair x = cos(t), y = cos(nt) gives the same first two properties scaled down by 2 but the polynomials leading coefficient is not 1 which is IMHO ugly. So that's why I like the scaled up versions.

Cool video Matt. You have set yourself Up for a Lot of parker square jokes though...

In the 1960's & '70's the Franklin Institute Science Museum in Philadelphia had an exhibit that drew Lissajous figures on a pair of 3 foot square tables using sand held in a large brass funnel. You could adjust one of the two lengths of the compound pendulums to get the various figures shown in this video. Back then a brass funnel 6" across wasn't considered either a theft risk or a safety risk. 80's kids proved them wrong and after several injuries and thefts (and countless repairs) the demonstration was removed. By the 1980's seeing rowdy kids climbing on the exhibit and swinging the funnels at each other didn't surprise me. I just couldn't figure out why the sand disappeared so fast. What was the fascination with play sand that drove so many kids to steal it.

Reminds me of of what you get from a spirograph. One way to improve it would be to have longer bolts (with a nut to hold the bolts vertical) then use multiple slats from each bolt alternating so the pen is held upright better.

I was playing around with the Speed Ratio (sr) on Matt's Spreadsheet in a similar manner as he did in the video. A few notable observations when 10 < sr < 127: sr=29, the red circle creates a cool pattern that is completely different than its surrounding sr=28 and sr=30 sr=31.665525, the red circle was completely filled in. sr>31.665525, the cycles start to revert back to the initial position sr=61.83151, the green cycle is almost a straight line sr=63.33105 (twice that of the previous sr), the red and green cycles are approximately the same as when sr=2 sr=126.6621 (twice that of the previous sr), all cycles are approximately the same as when sr=1 N.B. These are approximations made by brute force and a lot of spare time.

The midpoint figure created in the Excel sheet is a limacon Very similar to the math behind harmonic sequence components

I like how the near-missajous and ending music are sort of in time.

That's pretty cool!

Brought to you by Parker Square Engineering, Our bridges "almost" don't fall down.

Amazing...still a fan!

"Three good enough for Pi" Matt Parker 2018

the x and y coordinates for the second circle, B_x and B_y, respectively, use the radius of circle A (cell $B$3) rather than the cell for the radius of circle B

Nearmissajous! Love it!

That spreadsheet is perfectly replicating my signature!

What I find most interesting is how the 5/3 and 3/5 make the same pattern (with at 90* turn) but then 5/2 and 2/5 make such different pattens. 1:00

I can’t believe, he gets to spend his money on turning tables to create lines. This is the best job on the world.

Oh hey, Julio Mulero is one of my teachers, my programming teacher to be precise

You are a mad man!

You really did make a Parker Lissajous out of this.

Lissajous plots are pretty useful for measuring the relative phase of two signals of a particular integer frequency ratio. By using an oscilloscope and using one input channel as X, and one input channel as Y, you can determine the phase between the two signals by recording the x-y intersect points. While more modern equipment can typically measure phase of two signals of equal frequency, the Lissajous remains an effective method for measuring the phase of frequencies of integer ratio frequencies greater than 1.

As you were changing the values of the speed ratio, it was interesting to me to see that the number of loops in the midpoint pattern was equal to the speed ration -1 (as long as the speed ratio was an integer).

This just reminds me of the old Spirograph that I had as a kid back in the '80s.

"if you see a mistake, let me know" well, you did it in Excel to begin with.

What you made is a common geometric drawing machine. I forgot the specific name of it, and some people refer to it as a guilloché drawing machine; though that term will also bring up cycloidal drawing machines on google. Lissajous curves are different. They take the (x,y) point of circle A and (x,y) point of circle B, at a specific time interval with each circle having their own speed, and plot that intersection as a (x,y) point on a separate grid. There's no fixed length of the arms, and the arms have to stay parallel to which axis they represent; assuming circle A is to the side(s), it's arm would need to stay parallel to the X axis, as circle B would have to stay parallel to the Y axis, assuming circle B was to the top and/or bottom. This would be fixed by having two of each circle, circles A1 and A2 at the sides, and circles B1 and B2 at the top and bottom, and with hollow arms, the pen would always be in a position that is square to both axes. Only problem then would be tolerances. I remember seeing some mechanical etch-a-sketch machine that used pulleys on the two knobs, but this was years ago, and I don't remember if the pen was square to each axis or how tight tolerances were; but that is similar in concept but vastly different in implementation.

Matt reinvents a plotter machine.

Now that's quite a Parker Lissajous!

It might be in-topic for me to mention, a few years ago I took an online course on Alfred Hitchcock, and it was said the first computer graphics in a film might be the Lissajous curve drawn over Kim Novak's eye in the opening titles of "Vertigo". They used an old military thing.

the way that pen perfectly followed its previous path...

I love this guy, he always blows my brain😀

Argh Matt! Your tinkering set off my engineer’s OCD and I was about to bill you for a contribution to my therapy fees. But then you did your simulation in Excel, which restored my equilibrium. Phew!

In your excel plot of the mid-point, the patterns showing up at times reminds me of a video on the Mathologer channel called "Times Tables, Mandelbrot and the Heart of Mathmatics". He does times tables in a circle and gets the patterns.

Midpoint for 5 looked great.

The Parker Lissajous... putting in a lot of effort and trying really hard, only to just barely miss.

dude i would SO buy a Parker Curve shirt

This looks a LOT like @3Blue1Brown 's video about the geometric interpretation of the Fourier Transform! They both involve going around the circle with different speeds, so I suppose that makes sense.

Nice Parker Curve!

10:30 When Matt turns into an engineer

Oh I feel the need to get some lego out and make one of these now with little knobs to adjust the gearing to change the curve as it draws

If it is worth doing, it is worth overdoing :-) And now I have to open Python :-)

Nearmissajou is obviously the best name.

"I've got two turntables ..." Ohhhh, Beck was making lissajous curves!

There's a way to make these patterns with sand too....Its awesome! Watching mathematics in action!