PI DAY Build - A Binary Expansion of Pi

[TechnicBrickPower]

This Pi Day model demonstrates how to approximate a gearing ratio of Pi by representing Pi as a binary number and using differentials arranged in a chain formation to create the binary representation. Each differential implements 1 binary digit. If the binary digit is zero the differential can be replaced by a gearing ratio of a half to reduce the number of differentials required. This model has 23 binary digits and approximates Pi to 7 significant figures, uses 202 gears and is driven by a median PF motor.

 

 

[Jerry LEGO Creations]

Very interesting build!

[chlego]

Looks interesting! I am interested in how you got the idea though...

[TeamThrifty]

I love the merging of maths (with an 's', i'm english!!),and technic. This is such a powerful learning tool that would get engagement from even people who don't enjoy maths in its pure sense.. brilliant idea, explained and executed wonderfully. I thoroughly enjoyed this. Thanks for posting.

[Captainowie]

Yeah, but this (and your previous effort) relies on already knowing the value of Pi to some precision - you'd use exactly the same techniques to get a ratio of any rational number. Also, it's enormous.

I built a much more compact device that has a Pi:2 ratio, computed directly from the definition of Pi!

Aside: [removed]

Edited March 29, 2021 by Captainowie

[hollielucas]

15 hours ago, Captainowie said:

Yeah, but this (and your previous effort) relies on already knowing the value of Pi to some precision - you'd use exactly the same techniques to get a ratio of any rational number. Also, it's enormous.

I built a much more compact device that has a Pi:2 ratio, computed directly from the definition of Pi!

Aside: @TeamThrifty I grew up with "maths" in Australia, but I can't see any reason for the "s". Yes "mathematics" has the "s" at the end, but it's not like that's to indicate a plural (though it is derived from the greek "mathematikos" which _is_ plural, but you would always say "mathematics is", not "mathematics are") and when else do you slap the last letter of the original word back onto an abbreviation? Things like "Dr and Mrs Smith, who live on Drury Ln" don't count, because they are done for convenience of writing, not of speaking - you'd still pronounce it "Doctor and Misses Smith, who live on Drury Lane", not "Durr and Murrs Smith, who live on Drury Lunn".

Is there any need for this?

[TeamThrifty]

15 hours ago, Captainowie said:

Aside: @TeamThrifty I grew up with "maths" in Australia, but I can't see any reason for the "s".

Its maths in England... thats all i'm saying. Its not my opinion so no point lecturing me! In this country we call it Maths, not Math. 

[Captainowie]

13 hours ago, hollielucas said:

Is there any need for this?

You're right, probably not. Sorry @TeamThrifty, I didn't intend for it to come across as a lecture.

Edited March 29, 2021 by Captainowie

[TeamThrifty]

2 hours ago, Captainowie said:

You're right, probably not. Sorry @TeamThrifty, I didn't intend for it to come across as a lecture.

Its ok, i wasn't stressed about it - my reply probably didn't hit the right tone either! No drama's here 

[TechnicBrickPower]

On 3/28/2021 at 12:47 PM, Captainowie said:

Yeah, but this (and your previous effort) relies on already knowing the value of Pi to some precision - you'd use exactly the same techniques to get a ratio of any rational number. Also, it's enormous.

I built a much more compact device that has a Pi:2 ratio, computed directly from the definition of Pi!

Aside: @TeamThrifty I grew up with "maths" in Australia, but I can't see any reason for the "s". Yes "mathematics" has the "s" at the end, but it's not like that's to indicate a plural (though it is derived from the greek "mathematikos" which _is_ plural, but you would always say "mathematics is", not "mathematics are") and when else do you slap the last letter of the original word back onto an abbreviation? Things like "Dr and Mrs Smith, who live on Drury Ln" don't count, because they are done for convenience of writing, not of speaking - you'd still pronounce it "Doctor and Misses Smith, who live on Drury Lane", not "Durr and Murrs Smith, who live on Drury Lunn".

Hi @Captainowie, thanks for your reply. Hey yeah wow what you built is awesome - am still trying to figure out how it works...Is it really Pi:2? I didn't think that would be possible but you've done it. Thanks for sharing. What I am going to do next year for Pi Day!!? Also where I live it's mathz.

 

 

 

 

 

 

 

 

 

[Captainowie]

7 hours ago, TechnicBrickPower said:

Hi @Captainowie, thanks for your reply. Hey yeah wow what you built is awesome - am still trying to figure out how it works...Is it really Pi:2? I didn't think that would be possible but you've done it. Thanks for sharing. What I am going to do next year for Pi Day!!?

I probably should have shot a short vid, rather than rely on stills alone to show how it works. All it does is step a diameter around a circumference. For Pi diameters, you get one full rotation of the output (that's what Pi means), and one full rotation of the input crank steps two diameters, hence Pi:2.

The hardest part was keeping the "diameter" wheel in the same plane while still forcing it to keep contact with the "circumference" wheel - though I could probably have done a better job of it than I did here.

The precision of this is comes down to the ratio between the thickness of the wheel part and its diameter, which in this case is about 10%.

If you wanted to do a proper version next year, with an actual explanation and coordinated colour scheme, I wouldn't take offence!