Uploaded April 2022 | Updated September 2026, 2 weeks ago
Today is about reinventing a really cool mathematical wheel and its many different slide rule incarnations, just using a rubber band.
00:00 Intro
04:40 Multiply!
06:02 Pi times e
07:15 Divide!
08:39 Sliding rules
10:53 Apollo
11:08 Star Trek
11:45 Rubber band proof
13:13 Logarithms
16:50 Dmitry's wheel
17:48 Thank you!
This video was inspired by Dmitry Sagalovskiy's Wheel of logarithms. Here is his original animation:
dsagal.github.io/circle-of-fifths/logwheel
The source code lives here (free for you to modify)
github.com/dsagal/circle-of-fifths/blob/master/src/logcircle.ts
Dmitry's original post on Reddit with an interesting discussion section lives here:
tinyurl.com/4dc9hb2r
Dmitry's company Grist a spreadsheet-database product lives here:
getgrist.com
Must see, the amazing Slide Rule Simulator Emulator Replica Collection: Aristo, Faber-Castell, Pickett, ..., they are all there.
sliderules.org
Sadly, all these slide rules are linear slide rules. There are some circular slide rules apps made for mobile devices. However, I don't like any of them, except for the German WWII submarine Angriffsscheibe (=attack disk) app Sub Buddy which contains a circular slide rule (not free :(
It would be great if one of you could make a nice circular slide rule online app. Optional features could include: 1. input fields for numbers that are multiplied or divided and then the automatic execution of the slide rule actions with the scales spinning as in this video; 2. infinite precision by making it possible to zoom in on the scales and have it refine automatically; 3. tick box for squaring, as we rotate the two inputs for multiplying are kept the same; 4. incorporation of other look-up scales or even log-log scales; 5. Change of base. :)
The Wiki page on slide rules is excellent
en.wikipedia.org/wiki/Slide_rule
Don't miss out on the bottom of the page, especially the part on "Contemporary use".
Nice contributions to the Mathologer coding challenge (infinite precision zoomable circular slide rule)
Cristian Merighi: https://js.pacem.it/2d/circular-slide-ruler
Mike Wessler: phoenixave.com/crule
Liam Applebe: tiusic.com/slide_rule.html
Juan Ignacio Almenara Ortiz: desmos.com/calculator/tul8psjh32 (demos)
Root of evil math t-shirt: A missed opportunity squaring the root of evil using the circular slide rule to find evil :( Will do in my next life. Some of you commented that the number shown on the t-shirt was just truncated at the 4th decimal and not rounded. Well, strictly speaking it's wrong no matter whether you round or just chop off as the designer of this t-shirt did :)
Nice concise summary of why the circumference of the wheel is ln(10): At any given moment, the numerical scale of the unwrapped band is proportional to 1/x, where x is the number entering the wheel. So this is a really nice way to see that the integral of 1/x is a logarithmic function.
For real math gourmets: a slide rule for complex numbers :) demonstrations.wolfram.com/ComplexSlideRule
Sliderule nickname: Slipstick
Someone suggested another cute name: addalog computer (I like it :)
And another one: dial-log
Slide rule: only one child at a time (I like that one too :)
German: Rechenscheibe vs. Rechenschieber (calculating disk=circular slide rule vs. calculating slider=linear slide rule)
Check out what it took to win the international slide rule competition: sliderulemuseum.com/ISRC.htm
Different slide rule scales: quadibloc.com/math/sr02.htm (the whole site is really amazing quadibloc.com/math/slrint.htm)
A very detailed discussion of the use of circular slide rules in Star Trek: trekbbs.com/threads/props-re-used.81174/page-7
Circular slide rule in Dr Strangelove
tinyurl.com/35tkp6uj
https://www.fourmilab.ch/bombcalc/brico.html
youtube.com/watch?v=zZct-itCwPE
Slide rule in the movie Red October
tinyurl.com/4eehjp4p
Slide rule in the song Wonderful World by Sam Cooke
youtu.be/R4GLAKEjU4w?t=41
The largest slide rule (over 100 meters long!): mit-a.com/TexasMagnum.shtml
Something very interesting, a program for generating slide rule scales github.com/dylan-thinnes/slide-rules-generator
Connections to Vernier scales
aapt.scitation.org/doi/abs/10.1119/1.1991139?journalCode=ajp
patents.google.com/patent/US2424713A/en
Comment by TupperWallace: I’ll tell you why it was missed for hundreds of years: The rubber band wasn’t invented until St Patrick’s Day, 1845. The stretchy metaphor would not have been that understandable. :)
Real magic :) There are a few "easter eggs" hiding in this video which only the very observant will notice... e.g. youtu.be/ZIQQvxSXLhI?t=513
Music today: Trickster by Ian Post
Burkard
Today is about reinventing a really cool mathematical wheel and its many different slide rule incarnations, just using a rubber band.
00:00 Intro
04:40 Multiply!
06:02 Pi times e
07:15 Divide!
08:39 Sliding rules
10:53 Apollo
11:08 Star Trek
11:45 Rubber band proof
13:13 Logarithms
16:50 Dmitry's wheel
17:48 Thank you!
This video was inspired by Dmitry Sagalovskiy's Wheel of logarithms. Here is his original animation:
dsagal.github.io/circle-of-fifths/logwheel
The source code lives here (free for you to modify)
github.com/dsagal/circle-of-fifths/blob/master/src/logcircle.ts
Dmitry's original post on Reddit with an interesting discussion section lives here:
tinyurl.com/4dc9hb2r
Dmitry's company Grist a spreadsheet-database product lives here:
getgrist.com
Must see, the amazing Slide Rule Simulator Emulator Replica Collection: Aristo, Faber-Castell, Pickett, ..., they are all there.
sliderules.org
Sadly, all these slide rules are linear slide rules. There are some circular slide rules apps made for mobile devices. However, I don't like any of them, except for the German WWII submarine Angriffsscheibe (=attack disk) app Sub Buddy which contains a circular slide rule (not free :(
It would be great if one of you could make a nice circular slide rule online app. Optional features could include: 1. input fields for numbers that are multiplied or divided and then the automatic execution of the slide rule actions with the scales spinning as in this video; 2. infinite precision by making it possible to zoom in on the scales and have it refine automatically; 3. tick box for squaring, as we rotate the two inputs for multiplying are kept the same; 4. incorporation of other look-up scales or even log-log scales; 5. Change of base. :)
The Wiki page on slide rules is excellent
en.wikipedia.org/wiki/Slide_rule
Don't miss out on the bottom of the page, especially the part on "Contemporary use".
Nice contributions to the Mathologer coding challenge (infinite precision zoomable circular slide rule)
Cristian Merighi: https://js.pacem.it/2d/circular-slide-ruler
Mike Wessler: phoenixave.com/crule
Liam Applebe: tiusic.com/slide_rule.html
Juan Ignacio Almenara Ortiz: desmos.com/calculator/tul8psjh32 (demos)
Root of evil math t-shirt: A missed opportunity squaring the root of evil using the circular slide rule to find evil :( Will do in my next life. Some of you commented that the number shown on the t-shirt was just truncated at the 4th decimal and not rounded. Well, strictly speaking it's wrong no matter whether you round or just chop off as the designer of this t-shirt did :)
Nice concise summary of why the circumference of the wheel is ln(10): At any given moment, the numerical scale of the unwrapped band is proportional to 1/x, where x is the number entering the wheel. So this is a really nice way to see that the integral of 1/x is a logarithmic function.
For real math gourmets: a slide rule for complex numbers :) demonstrations.wolfram.com/ComplexSlideRule
Sliderule nickname: Slipstick
Someone suggested another cute name: addalog computer (I like it :)
And another one: dial-log
Slide rule: only one child at a time (I like that one too :)
German: Rechenscheibe vs. Rechenschieber (calculating disk=circular slide rule vs. calculating slider=linear slide rule)
Check out what it took to win the international slide rule competition: sliderulemuseum.com/ISRC.htm
Different slide rule scales: quadibloc.com/math/sr02.htm (the whole site is really amazing quadibloc.com/math/slrint.htm)
A very detailed discussion of the use of circular slide rules in Star Trek: trekbbs.com/threads/props-re-used.81174/page-7
Circular slide rule in Dr Strangelove
tinyurl.com/35tkp6uj
https://www.fourmilab.ch/bombcalc/brico.html
youtube.com/watch?v=zZct-itCwPE
Slide rule in the movie Red October
tinyurl.com/4eehjp4p
Slide rule in the song Wonderful World by Sam Cooke
youtu.be/R4GLAKEjU4w?t=41
The largest slide rule (over 100 meters long!): mit-a.com/TexasMagnum.shtml
Something very interesting, a program for generating slide rule scales github.com/dylan-thinnes/slide-rules-generator
Connections to Vernier scales
aapt.scitation.org/doi/abs/10.1119/1.1991139?journalCode=ajp
patents.google.com/patent/US2424713A/en
Comment by TupperWallace: I’ll tell you why it was missed for hundreds of years: The rubber band wasn’t invented until St Patrick’s Day, 1845. The stretchy metaphor would not have been that understandable. :)
Real magic :) There are a few "easter eggs" hiding in this video which only the very observant will notice... e.g. youtu.be/ZIQQvxSXLhI?t=513
Music today: Trickster by Ian Post
Burkard
