Metric vs. other measurement systems - chart

[mklotz]

If you use rational fraction approximations for pi, the Tsu Chi form, 355/113, is far more accurate than 22/7. There are other approximations that are even more accurate as this extract from my notes shows...

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APPROXIMATING PI = 3.1415926535898

Biblical approximation: 3 (4.5%)

"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26

22 / 7 = 3.142857142857 (0.04 %)

22 / 7.0028 = 3.141600502656 (0.00025 %)

Tsu Chung Chi approximation: 355 / 113 = 3.141592920354 (0.0000085 %)

Euler: 103993 / 33102 = 3.141592653012 (-0.000000018 %)

Ramanujan's improvement to Chi: (355 / 113) * (1 - 0.0003 / 3533) = 3.14159265359 (below calculator range)

Ramanujan's first term in fast series for pi: 9801 / [1103 * sqrt(8)] = 3.141592730013 (0.0000024 %)

Ramanujan: (63 / 25) * [(17 + 15 * sqrt(5)) / (7 + 15 * sqrt(5))] = 3.141592653806 (0.000000007 %)

Fourth root: (2143 / 22)^(1/4) = 3.14159265258 (-0.000000032 %)

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Four bangers, despite having a square root key, usually lack the far more useful pi key, so knowing some easy approximations is a good thing.



Newton's technique of iterating to find other roots can easily be generalized. For the nth root of N, the equation is:

x2 = [(n - 1)*x1 + N/x1^(n-1)]/n

which, for n = 2, reduces to the equation shown in my previous post.

The convergence is at least quadratic in a neighborhood of the zero, which intuitively means that the number of correct digits roughly doubles in every step. For faster convergence, one can use Halley's method which exhibits cubic convergence.

[Elizabeth Greene]

Americans will do anything to avoid using the metric system.

[mklotz]

Americans will do anything to avoid using the metric system.

They know that, if the USA actually started using the metric system, they would have TWO measurement systems they don't understand.

[Crusty]

They have to add those stupid labels so that they have a positive defense in any lawsuit from opportunists looking for a payout.

[mklotz]

They have to add those stupid labels so that they have a positive defense in any lawsuit from opportunists looking for a payout.

The fact that the shade manufacturer can be sued for accidents caused by driving with the shade in place is a clear demonstration of the failed average intelligence. In an educated society, such crap wouldn't be considered; the case would be thrown out of court.

[Frank S]

The fact that the shade manufacturer can be sued for accidents caused by driving with the shade in place is a clear demonstration of the failed average intelligence. In an educated society, such crap wouldn't be considered; the case would be thrown out of court.

Why do you think new cars have collision avoidance braking and lane wandering sensors, now days? and automatic parallel parking or controlled trailer backing. Heck people have to have an app on their phone to start their cars, tell them when they might be running low on gas and the phone has to interface with the vehicle at all times so it will know where to go to get a tire aired up or the car itself is a roving wifi connected to the web at all times

[Crusty]

I don't place the blame for that on people in general, despite their apparent reptilian understanding, but rather on the legal system. The legal system, designed by and for lawyers, was created to entangle people so that they may be fleeced for the benefit of lawyers, and they've made incremental progress over the years using the government to force their system onto potentially everyone. It's all about taking universally understood concepts and spinning them into something which can be exploited for financial gain.

Product liability laws come from this system, where the phrase "reasonable and prudent" is a big money maker. It's a grand scam in which justice is only an occasional by-product.


E.G. "That depends on what your definition of "is" is. WJ Clinton

[hemmjo]

I don't place the blame for that on people in general, despite their apparent reptilian understanding, but rather on the legal system. The legal system, designed by and for lawyers, was created to entangle people so that they may be fleeced for the benefit of lawyers, and they've made incremental progress over the years using the government to force their system onto potentially everyone. It's all about taking universally understood concepts and spinning them into something which can be exploited for financial gain.

Product liability laws come from this system, where the phrase "reasonable and prudent" is a big money maker. It's a grand scam in which justice is only an occasional by-product.


E.G. "That depends on what your definition of "is" is. WJ Clinton

The REALLY scary things is, the vast majority of our elected officials are lawyers!!!!

[Toolmaker51]

The REALLY scary things is, the vast majority of our elected officials are lawyers!!!!

Of course; they have gamed their own system [converting justice and civil law into legal manipulations], so politics is just another avenue straight to Agendaville.

I've said this forever; most [maybe all] the inequities we suffer as citizens are traceable to lawyers, lobbyists and politicians. I don't single out the left broadly, yet far left certainly is the keystone. Added detail, lawyers have only studied the law, attorneys pass bar examinations.

For example; they'll inform you otherwise about that hierarchy; I reply with one or another challenge but favorite is, "how many interpretations are there to Shall Not Be Infringed...". They'll argue meaning of militia, I remind them of Minute Man statue and his pose, in Concord, Mass., even name implies differently then standing army.
Stops them every time.

[12L14]

The REALLY scary things is, the vast majority of our elected officials are lawyers!!!!

And now imagine place where most of those officials are engineers(lets say F. W. Taylor type smart scumbags).

Sounds like science fiction?

Think again.

Commie china, east Germany and(to some extension) soviet union are/were "good" examples of such places...