Why is 3/14 called pi day and 7/22 called pi *approximation* day when 22/7 is actually closer to π than 3.14 is?

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I guess arguably March 14th covers the interval [3.14, 3.15)

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π is roughly 137.61 seconds into March 14th.

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22/7 is roughly 109.25 "seconds" off π (measured in "March time" of 0.01 = 24 hours)

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But if you consider it's only 22/7 at midnight on July 22nd, then when is π in July?

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π × 7 is roughly 21.9911485751 which is 0.0088514248714 off "midnight".

This is actually 12.746 *minutes*.

Things move much more quickly in July (where each day is 1/7th) compared with March (where each day is 0.01)

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So:

π in March is roughly 00:02:17.61 on March 14th.

π in July is roughly 23:47:15.24 on July 21st.



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So arguably at no point on July 22nd are you closer to π than at the same time on March 14th.

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Inspired by [Colin Wright](https://twitter.com/colinthemathmo), here's a Python list comprehension working out the top 10 date approximations:

from math import pi

```
print [i[1] for i in sorted([
    (abs(pi - (day + 1.) / (month + 1)), "{}/{}".format(day + 1, month + 1))
    for month in range(12)
    for day in range([31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31][month])
])[:10]]
```

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Which gives the answer:

```
['22/7', '25/8', '19/6', '28/9', '31/10', '16/5', '29/9', '13/4', '26/8', '12/4']
```

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Inspired by [Paul Salomon](https://twitter.com/lostinrecursion), here are the "pi-times" each month:

```
3/1 03:23:53
6/2 06:47:47
9/3 10:11:40
12/4 13:35:34
15/5 16:59:28
18/6 20:23:21
21/7 23:47:15
25/8 03:11:08
28/9 06:35:02
31/10 09:58:56
```

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The above is somewhat of a sleight of hand because we're treating the time as 0-indexed but the day as 1-indexed. In other words, the first moment of July is considered to already be 1/31 of the way in and the last moment is considered 32/7.

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But hey, the majority of the world thought the millennium started in 2000 right? :-)