- #1
juantheron
- 243
- 1
Calculation of $57^{th}$ digit in the decimal expansion of $\displaystyle \frac{1}{57}$
MHB 57^(th) digit in decimal expansion
- Thread starter juantheron
- Start date
Click For Summary
The discussion focuses on calculating the 57th digit in the decimal expansion of 1/57. It highlights the use of modular arithmetic and Euler's phi function to determine the period of the decimal expansion. By finding the period, one can compute earlier digits in the sequence, simplifying the process. The approach emphasizes efficiency in calculating specific digits without needing to compute the entire decimal expansion. Understanding these mathematical tools is crucial for accurately determining the desired digit.
Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...
Similar threads
- · Replies 7 ·
- · Replies 15 ·
- · Replies 54 ·
- · Replies 2 ·
- · Replies 15 ·
- · Replies 1 ·
- · Replies 2 ·
- · Replies 1 ·