Easy as Pi

[Michael GilliganParticipant @michaelgilligan61133]

This is not actually about Clocks or Scientific Instruments as such … but about one of the ‘impossible problems’ of antiquity.

The series of videos develops from first principles into Archimedes’ elegant method of approximation.

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I found it fascinating and well-presented

… Others may, or may not !

MichaelG.

 

[Kiwi BlokeParticipant @kiwibloke62605]

Thanks, Michael, always interesting to follow your links. No wish to steal your thunder, however I thought the rather pedestrian video was going to be about the pi = 4 paradox, but it wasn’t… This is the paradox that if a square of side length = 1 is drawn around a circle of diameter = 1, it has a perimeter = 4, whereas the circle’s circumference = pi. Obvious. But if you draw the same ‘circle’, (equivalent to ‘folding in’ the corners of the square, and then the corners of the resulting figure, over and over), with the ‘pen’ constrained to move orthogonally, even as the steps in the approximate circle become vanishingly small, and the trace appears to be a macroscopically smooth circle, its perimeter obstinately stays equal to 4. Counterintuitive – at least for my aged and enfeebled brain…

[John HaineParticipant @johnhaine32865]

The operative words are “appears to be” but if you looked at a microscopic section of the periphery it would always be made of square steps either side of the true circle, whatever the magnification. No paradox.

[Kiwi Bloke]

On Kiwi Bloke Said:

… rather pedestrian video …

True, but it probably duplicates what he teaches in class … and it certainly gets the basic points across clearly.

Although most of us are familiar with the Archimedes method using the inscribed polygon, I was pleased to see [in the third video] him discuss the circumscribed one.

MichaelG.

[John Haine]

On John Haine Said:

The operative words are “appears to be” but if you looked at a microscopic section of the periphery it would always be made of square steps either side of the true circle, whatever the magnification. No paradox.

The name Slartibartfast springs to mind 🙂

MichaelG.

[duncan webster 1Participant @duncanwebster1]

Nerds like me might find this interesting, it’s how Archimedes arrived at his value for pi. What the website doesn’t tell you is the vital bit of information that from Pythagoras cos(30) =  sqrt(3)/2  and cos(angle/2) = sqrt((1+cos(angle))/2).

You can see there’s nothing on telly worth watching, and I’ve had grandchildren all evening so I’m whacked!

[duncan webster 1Participant @duncanwebster1]

Nerds like me might find this interesting, it’s how Archimedes arrived at his value for pi. What the website doesn’t tell you is the vital bit of information that from Pythagoras cos(30) =  sqrt(3)/2  and cos(angle/2) = sqrt((1+cos(angle))/2).

You can see there’s nothing on telly worth watching, and I’ve had grandchildren all evening so I’m whacked!

[duncan webster 1]

On duncan webster 1 Said:

Nerds like me might find this interesting, it’s how Archimedes arrived at his value for pi. What the website doesn’t tell you is the vital bit of information that from Pythagoras cos(30) =  sqrt(3)/2  and cos(angle/2) = sqrt((1+cos(angle))/2).

You can see there’s nothing on telly worth watching, and I’ve had grandchildren all evening so I’m whacked!

Double post, can a mod remove thanks

[michael mParticipant @michaelm]

And remember, that whilst to eat a whole cake is the sin of gluttony,

The sin of pie is zero!

[Author]

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