MHB Value of Irrational Number π (Part 1)

AI Thread Summary
The value of the irrational number π is approximately 3.1415926535, accurate to ten decimal places. The discussion revolves around determining how closely the quantity (4/3)^4, which is derived from the Rhind papyrus, approximates π. Participants explore whether this calculation can be performed without a calculator, suggesting the use of long division to compute (4/3)^4 as 256/81. The conversation emphasizes the need for clarity in the original question to avoid confusion. Ultimately, the goal is to establish the decimal agreement between (4/3)^4 and π.
mathdad
Messages
1,280
Reaction score
0
The value of irrational number π, correct to ten decimal places (without rounding), is 3.1415926535. By using your calculator, determine to how many decimal places the following quantity [(4/3)^4] agrees with π.

The value used for π in the Rhind papyrus, an ancient Babylonian text written about 1650 B.C. is (4/3)^4.

I was wondering if this question can be answered without a calculator. Can we show that (4/3)^4 in terms of decimal places agrees with pi?
 
Last edited:
Mathematics news on Phys.org
Where do you need help with this problem?
 
Evgeny.Makarov said:
Where do you need help with this problem?

I was wondering if this question can be answered without a calculator. Can we show that (4/3)^4 in terms of decimal places agrees with pi?
 
RTCNTC said:
I was wondering if this question can be answered without a calculator.
Then this should be said in the original question to not make people guess.

RTCNTC said:
Can we show that (4/3)^4 in terms of decimal places agrees with pi?
You can use long division to compute $$\left(\frac43\right)^4=\frac{256}{81}$$ to a few decimal places.
 
Evgeny.Makarov said:
Then this should be said in the original question to not make people guess.

You can use long division to compute $$\left(\frac43\right)^4=\frac{256}{81}$$ to a few decimal places.

The original question has been edited.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
4
Views
2K
Replies
4
Views
2K
Replies
1
Views
2K
Replies
12
Views
2K
Replies
11
Views
3K
Replies
4
Views
3K
Replies
8
Views
2K
Back
Top