Programmer's Clock

Programmer's Clock

Recently found a "math clock" about programmers, which is very popular in the following picture:

Previously, only 11 o ' clock analysis was known; for 3 o'clock, there was no train of thought. So he sent a circle of friends to help God explain the 3 o'clock. Under the guidance of Liu Zixi, Jahuson, liming and other great gods, he understood what was going on. So here are the 12 points that should be explained. Personal opinion, for reference only. 12 pips

Needless to say, 1728 of the cubic root. 1 Pips

Many people may not know that this is the Legendre constant:

$\lim_{x \rightarrow +\infty} {ln (x) –\frac{x}{\pi (x)}}$

where the $\PI (x) $ represents the number of primes not greater than X, which can be approximated by $\frac{x}{lnx}$.

This value after Legendre, Gauss and other a number of math big guy's efforts, and finally by the mathematician Charles Jean proved to be 1. 2 pips

The sum of infinite recursive geometric progression, the first item is 1, the male ratio is $\frac{1}{2}$, so it's and for

S = $\frac{a_1}{1-q}$ = 2 3 points

In Liu Zixi, Jahuson, liming and other great God's help, finally know.

Widely used in XML, HTML. & #后面接十进制字符,& #x后面接十六进制字符. Equivalent to an escape sequence.

Where hex 33 is equal to decimal 51, which is ' 3 '. 4 pips

Congruence problem (Modular multiplicative inverse)

Make

$x \equiv2^{-1} mod 7$

$2X\EQUIV1 MoD 7$

$x = 4$ 5 points

$\phi$ represents the Golden section ratio, $\phi = \frac{\sqrt{5}–1}{2} $

The Golden section appears in the general formula of the Fibonacci sequence.

But this place, I do not understand, do not know whether this is not the author of this picture of the error. Personally think it should be $ (2\phi+1) ^2$ instead of $ (2\phi-1) ^2$ 6 pips

Needless to say, factorial. 7 pips

Represents 6.999999999 ... Where 9 of the head is on a horizontal, indicating that the loop section is 9.

So, 6.9999 .... Why is it equal to 7? Well, or infinite recursive geometric progression angle of view to consider, it is suitable for all ages.

6.9999...= 6 + 0.9 + 0.09 + 0.009 + 0.0009 + ...

The one in the back.

0.9 + 0.09 + 0.009 + 0.0009 + ...

The first item is 0.9, the male ratio is 0.1, and the convergence is 1.

So 6.9999 = 7 8 points

Represents 1000 (binary), because only the first one is bright and the others are dark. (Light is 1, dark for 0,bitmap feeling.) may be Braille), so it is 8. 9 Pips

Four-in-the-system. 21 (quad) = 2 * 4 + 1 = 9. 10 pips

Number of combinations, 5! /(2! * 3!) = 11 points

Hex, A is 10,b is 11,c is 12. Note, note that this is 0x0b, not 0x08. Ha ha.

Reviews: Knowledge points are a bit repetitive, for example, there are several in the system. Give a good comment, but not five-star.