Linear Digit Square to Curve Transformation in 2D Space

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Just a random hypothesis that I had in how a curved shaded area could be equal to a rectangular shaded area. Not even sure it works in 2D Space let alone 3D Space. If you need a further explanation just message me

[studiot]

 

Just a random hypothesis that I had in how a curved shaded area could be equal to a rectangular shaded area. Not even sure it works in 2D Space let alone 3D Space. If you need a further explanation just message me

 

Speculations belong in the speculation forum and discussions within the thread itself.

 

 

 

However this may not be an idle hypothesis, unlike so many that are posted.

That would be highly refreshing.

 

There used to be a recognised technique for graphical integration, directly from the curve, in the days before calculators.

It may have similarities to your idea.

 

So post proper details for discussion by all.

Edited May 22, 2016 by studiot

[Bignose]

There used to be a recognised technique for graphical integration, directly from the curve, in the days before calculators.

Including the classic graph your curve on graph paper. Then cut out your curve and weigh it on a sensitive balance. And then weigh a known rectangle cut from the same paper. Certainly not perfect, but pretty decent method before numerical integration was feasible to a lot of people.

[studiot]

Yes some form of 'counting the squares' has always been available, but I was not thinking of that.

 

And regular drafting offices did not used to have sensitive balances as part of their stock equipment, but they may have had a planimeter (which I was not thinking of either).

Edited May 22, 2016 by studiot

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Thank you all for the insight, I was unsure in which direction to go with this. It is nice to be given advice from both an expert and a senior member.