explain xkcd - User contributions [en]

1685: Patch

2016-05-25T06:05:53Z

108.162.214.143: /* Explanation */

{{comic
| number = 1685
| date = May 25, 2016
| title = Patch
| image = patch.png
| titletext = My optimizer uses content-aware inpainting to fill in all the wasted whitespace in the code, repeating the process until it compiles.
}}

==Explanation==
{{incomplete|Created by a BOT - Please change this comment when editing this page.}}

Adobe Photoshop is a commonly used software for image manipulation. One of its features is "content-aware inpainting", which allows the user to delete parts of the image and seamlessly replacing the deleted sections with "patches" of texture from other parts of the image. GNU patch is a software program that replaces only parts of the code with an updated version, without requiring the user to download the entire source code. Here, it appears the was told to "patch" the code, but used Photoshop to do this instead of GNU patch, with devastating results.

==Transcript==
{{incomplete transcript|Intitial transcript.}}
[A screenshot of a part of a code, rendered unreadable due to image editing.]

Protip: If you don't have access to the GNU ''patch'' tool, you can use the Photoshop one.

{{comic discussion}}

[[Category:Protip]]
[[Category:Programming]]

1685: Patch

2016-05-25T06:02:57Z

108.162.214.143: /* Explanation */

{{comic
| number = 1685
| date = May 25, 2016
| title = Patch
| image = patch.png
| titletext = My optimizer uses content-aware inpainting to fill in all the wasted whitespace in the code, repeating the process until it compiles.
}}

==Explanation==
{{incomplete|Created by a BOT - Please change this comment when editing this page.}}

Adobe Photoshop is a commonly used software for image manipulation. One of its features is "content-aware inpainting", which allows the user to delete parts of the image and seamlessly replacing the deleted sections with "patches" of texture from other parts of the image.

GNU Patch is a software program that replaces only parts of the code with an updated version, without requiring the user to download the entire source code.

==Transcript==
{{incomplete transcript|Intitial transcript.}}
[A screenshot of a part of a code, rendered unreadable due to image editing.]

Protip: If you don't have access to the GNU ''patch'' tool, you can use the Photoshop one.

{{comic discussion}}

[[Category:Protip]]
[[Category:Programming]]

1685: Patch

2016-05-25T06:02:23Z

108.162.214.143: /* Explanation */

{{comic
| number = 1685
| date = May 25, 2016
| title = Patch
| image = patch.png
| titletext = My optimizer uses content-aware inpainting to fill in all the wasted whitespace in the code, repeating the process until it compiles.
}}

==Explanation==
{{incomplete|Created by a BOT - Please change this comment when editing this page.}}

Adobe Photoshop is a commonly used software for image manipulation. One of its features is "content-aware inprinting", which allows the user to delete parts of the image and seamlessly replacing the deleted sections with "patches" of texture from other parts of the image.

GNU Patch is a software program that replaces only parts of the code with an updated version, without requiring the user to download the entire source code.

==Transcript==
{{incomplete transcript|Intitial transcript.}}
[A screenshot of a part of a code, rendered unreadable due to image editing.]

Protip: If you don't have access to the GNU ''patch'' tool, you can use the Photoshop one.

{{comic discussion}}

[[Category:Protip]]
[[Category:Programming]]

Talk:1656: It Begins

2016-03-17T21:20:06Z

108.162.214.143:

It Begins:
:[http://money.cnn.com/2016/03/15/media/oscars-chris-rock-asian-jokes/index.html Oscar apologizes]!
Did it work? :-) --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 08:50, 16 March 2016 (UTC)

:This brings the question how often would comment "It Begins" be labeled as offensive, for example racist or something ... and, unfortunately, that already begun years ago. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 11:48, 16 March 2016 (UTC)

It has been quite a while since the last [[:Category:Protip|Protip]], except for the [http://www.explainxkcd.com/wiki/images/5/50/1608_1048x1074y_Pyramid_protip.png pyramid pro tip] in [[1608: Hoverboard]], it is almost 100 comics since the last real protip comic: [[1565: Back Seat]]. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 09:08, 16 March 2016 (UTC)

This makes me think of the beginning of [https://en.wikipedia.org/wiki/The_Birds_%28film%29 The Birds]. I do not know if it is intended. -- [[User:InviPinkUnicorn|InviPinkUnicorn]] ([[User talk:InviPinkUnicorn|talk]]) 11:44, 16 March 2016 (UTC)
: I think it unmistakably is a reference to the Hitchcock film, especially given the specific choice of seagulls. I changed the explanation, but left the other possibilities in. [[User:Miamiclay|Miamiclay]] ([[User talk:Miamiclay|talk]]) 22:03, 16 March 2016 (UTC)
The bird's behavior is pretty normal, gulls break clam shells and such by dropping them on to the beach. Maybe it was a clam shell phone? [[Special:Contributions/108.162.245.180|108.162.245.180]] 15:21, 16 March 2016 (UTC)

In my opinion the explanation is missing one important use of "It begins": fearmongering. I follow a far-right website just to keep oriented (and sometimes entertained) about far-right political views, and the guy who runs the site typically runs at least one story a week with the title starting with "It begins:". Some examples: "It Begins… Obama Plays Race Card Against Trump – Attacks White Working Class", "It Begins… Obama’s HUD Launches Civil Rights Investigation on IL Town for Not Building Public Housing", "It Begins… Democrat Lawmaker Proposes $100 Tax on Every Gun", "It Begins… Outraged Flea Market Shopper Calls Cops Over Confederate Memorabilia", etc. etc. --[[User:RenniePet|RenniePet]] ([[User talk:RenniePet|talk]]) 20:12, 16 March 2016 (UTC)

;Missing reference?

The "in bed" meme, as detailed in [[425:_Fortune_Cookies]] [[Special:Contributions/198.41.235.233|198.41.235.233]] 21:55, 16 March 2016 (UTC)

It begins.

[http://www.foxnews.com/politics/2016/03/17/ryan-says-open-gop-convention-more-likely.html Ryan says open GOP convention 'more likely'] --[[Special:Contributions/108.162.214.143|108.162.214.143]] 21:19, 17 March 2016 (UTC)

Talk:1656: It Begins

2016-03-17T21:19:20Z

108.162.214.143:

It Begins:
:[http://money.cnn.com/2016/03/15/media/oscars-chris-rock-asian-jokes/index.html Oscar apologizes]!
Did it work? :-) --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 08:50, 16 March 2016 (UTC)

:This brings the question how often would comment "It Begins" be labeled as offensive, for example racist or something ... and, unfortunately, that already begun years ago. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 11:48, 16 March 2016 (UTC)

It has been quite a while since the last [[:Category:Protip|Protip]], except for the [http://www.explainxkcd.com/wiki/images/5/50/1608_1048x1074y_Pyramid_protip.png pyramid pro tip] in [[1608: Hoverboard]], it is almost 100 comics since the last real protip comic: [[1565: Back Seat]]. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 09:08, 16 March 2016 (UTC)

This makes me think of the beginning of [https://en.wikipedia.org/wiki/The_Birds_%28film%29 The Birds]. I do not know if it is intended. -- [[User:InviPinkUnicorn|InviPinkUnicorn]] ([[User talk:InviPinkUnicorn|talk]]) 11:44, 16 March 2016 (UTC)
: I think it unmistakably is a reference to the Hitchcock film, especially given the specific choice of seagulls. I changed the explanation, but left the other possibilities in. [[User:Miamiclay|Miamiclay]] ([[User talk:Miamiclay|talk]]) 22:03, 16 March 2016 (UTC)
The bird's behavior is pretty normal, gulls break clam shells and such by dropping them on to the beach. Maybe it was a clam shell phone? [[Special:Contributions/108.162.245.180|108.162.245.180]] 15:21, 16 March 2016 (UTC)

In my opinion the explanation is missing one important use of "It begins": fearmongering. I follow a far-right website just to keep oriented (and sometimes entertained) about far-right political views, and the guy who runs the site typically runs at least one story a week with the title starting with "It begins:". Some examples: "It Begins… Obama Plays Race Card Against Trump – Attacks White Working Class", "It Begins… Obama’s HUD Launches Civil Rights Investigation on IL Town for Not Building Public Housing", "It Begins… Democrat Lawmaker Proposes $100 Tax on Every Gun", "It Begins… Outraged Flea Market Shopper Calls Cops Over Confederate Memorabilia", etc. etc. --[[User:RenniePet|RenniePet]] ([[User talk:RenniePet|talk]]) 20:12, 16 March 2016 (UTC)

;Missing reference?

The "in bed" meme, as detailed in [[425:_Fortune_Cookies]] [[Special:Contributions/198.41.235.233|198.41.235.233]] 21:55, 16 March 2016 (UTC)
It begins.

[http://www.foxnews.com/politics/2016/03/17/ryan-says-open-gop-convention-more-likely.html Ryan says open GOP convention 'more likely'] --[[Special:Contributions/108.162.214.143|108.162.214.143]] 21:19, 17 March 2016 (UTC)

1047: Approximations

2016-03-14T04:53:39Z

108.162.214.143:

{{comic
| number = 1047
| date = April 25, 2012
| title = Approximations
| image = approximations.png
| titletext = Two tips: 1) 8675309 is not just prime, it's a twin prime, and 2) if you ever find yourself raising log(anything)^e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong.
}}

==Explanation==
This comic lists some approximations for numbers, most of them mathematical and physical constants, but some of them jokes and cultural references.

Approximations like these are sometimes used as {{w|mnemonic}}s by mathematicians and physicists, though most of Randall's approximations are too convoluted to be useful as mnemonics. Perhaps the best known mnemonic approximation (though not used here by Randall) is that "pi is approximately equal to 22/7". Randall does mention (and mock) the common mnemonic among physicists that the {{w|fine structure constant}} is approximately 1/137. Although Randall gives approximations for the number of seconds in a year, he does not mention the common physicist's mnemonic that it is "pi times 10^7," though he later added a statement to the top of the comic page addressing this point.

At the bottom of the comic are expressions involving {{w|transcendental numbers}} (namely pi and e) that are tantalizingly close to being exactly true but are not (indeed, they cannot be, due to the nature of transcendental numbers). Such near-equations were previously discussed in [[217: e to the pi Minus pi]]. One of the entries, though, is a "red herring" that is exactly true.

Randall says he compiled this table through "a mix of trial-and-error, ''{{w|Mathematica}}'', and Robert Munafo's [http://mrob.com/pub/ries/ Ries] tool. "Ries" is a "{{w|Closed-form expression#Conversion from numerical forms|reverse calculator}}" that forms equations matching a given number.

The first part of the title text notes that "Jenny's constant," which is actually a telephone number referenced in Tommy Tutone's 1982 song {{w|867-5309/Jenny}}, is not only prime but a {{w|twin prime}} because 8675311 is also a prime. Twin primes have always been a subject of interest, because they are comparatively rare, and because it is not yet known whether there are infinitely many of them. Twin primes were also referenced in [[1310: Goldbach Conjectures]].

The second part of the title text makes fun of the unusual mathematical operations contained in the comic. {{w|Pi}} is a useful number in many contexts, but it doesn't usually occur anywhere in an exponent. Even when it does, such as with complex numbers, taking the pi-th root is rarely helpful. Similarly, {{w|e (mathematical constant)|e}} typically appears in the basis of a power (forming the {{w|exponential function}}), not in the exponent. (This is later referenced in [http://what-if.xkcd.com/73/ Lethal Neutrinos]).

:{| class="wikitable"
|-
|align="center"|Thing to be approximated:
|align="center"|Formula proposed:
|align="center"|Resulting approximate value:
|align="center"|Correct value:
|align="center"|Discussion:
|-
|align="center"|One light year(m)
|align="center"|998
|align="center"|9,227,446,944,279,201
|align="center"|9,460,730,472,580,800 (exact)
|align="left"|998 and 698 are sexual references.
|-
|align="center"|Earth Surface(m2)
|align="center"|698
|align="center"|513,798,374,428,641
|align="center"|5.10072*1014
|align="left"|998 and 698 are sexual references.
|-
|align="center"|Ocean's volume(m3)
|align="center"|919
|align="center"|1,350,851,717,672,992,089
|align="center"|1,332*1018
|align="left"|
|-
|align="center"|Seconds in a year
|align="center"|754
|align="center"|31,640,625
|align="center"|31,557,600 (Julian calendar) 31,556,952 (Gregorian calendar)
|align="left"|After this comic was released [[Randall]] got many responses by viewers. So he did add this statement to the top of the comic page:
"Lots of emails mention the physicist favorite, 1 year = pi x 107 seconds. 754 is a hair more accurate, but it's hard to top 3,141,592's elegance." Pi x 107 is nearly equal to 31,415,926.536, and 754 is exactly 31,640,625. Randall's elegance belongs to the number pi, but it should be multiplied by the factor of ten.

Using the traditional definitions that a second is 1/60th of a minute, a minute is 1/60th of an hour, and an hour is 1/24th of a day, a 365-day year is exactly 31,536,000 seconds (the "for rent method" approximation). Until the calendar was reformed by Pope Gregory, there was one leap year in every four years, making the average year 365.25 days, or 31,557,600. On the current calendar system, there are only 97 leap years in every 400 years, making the average year 365.2425 days, or 31,556,952 seconds. In technical usage, a "second" is now defined based on physical constants, even though the length of a day varies inversely with the changing angular velocity of the earth. To keep the official time synchronized with the rotation of the earth, a "leap second" is occasionally added, resulting in a slightly longer year.
|-
|align="center"|Seconds in a year (rent method)
|align="center"|525,600 x 60
|align="center"|31,536,000
|align="center"|31,557,600 (Julian calendar) 31,556,952 (Gregorian calendar)
|align="left"|"Rent Method" refers to the song "Seasons of Love" from the musical "{{w|Rent (musical)|Rent}}." The song asks, "How do you measure a year?" One line says "525,600 minutes" while most of the rest of the song suggests the best way to measure a year is moments shared with a loved one.
|-
|align="center"|Age of the universe (seconds)
|align="center"|1515
|align="center"|437,893,890,380,859,375
|align="center"|4.354±0.012*1017 (best estimate; exact value unknown)
|align="left"|
|-
|align="center"|Planck's constant
|align="center"|1/(30πe)
|align="center"|6.68499014108082*10−34 (rounded)
|align="center"|6.62606957*10−34
|align="left"|Informally, the {{w|Planck constant}} is the smallest action possible in quantum mechanics.
|-
|align="center"|Fine structure constant
|align="center"|1/140
|align="center"|0.00714285717142857171428571, etc. (repeating 71428571)
|align="center"|0.00729735257 (accepted value as of 2011), close to 1/137
|align="left"|The {{w|fine structure constant}} indicates the strength of electromagnetism. It is unitless and around 0.007297, close to 1/137. At one point it was believed to be exactly the reciprocal of 137, and many people have tried to find a simple formula explaining this (with a pinch of {{w|numerology}} thrown in at times), including the infamous {{w|Arthur Eddington|Sir Arthur Adding-One}}.
|-
|align="center"|Fundamental charge
|align="center"|3/(14 * πππ)
|align="center"|1.59895121062716*10−19 (rounded)
|align="center"|1.602176565*10−19 (rounded)
|align="left"|This is the charge of the proton, symbolized "e" for electron (whose charge is actually -e. You can blame Benjamin Franklin [[567|for that]])
|-
|align="center"|Telephone number for the White House Switchboard
|align="center"|1/ 
π√(e(1 + (e-1)√8))
|align="center"|.2024561414 (truncated)
|align="center"|2024561414
|align="left"|
|-
|align="center"|Jenny's Constant
|align="center"|(7(e/1 - 1/e) - 9) * π2
|align="center"|867.530901981685 (approximately)
|align="center"|8675309
|align="left"|"Jenny's constant" is actually a telephone number referenced in Tommy Tutone's 1982 song {{w|867-5309/Jenny}}. As mentioned in the title text, the number not only prime but a {{w|twin prime}} because 8675311 is also a prime.
|-
|align="center"|World Population Estimate (billions)
|align="center"|Equivalent to 6+((3/4 Year + 1/4 (Year mod 4) - 1499)/10) billion
|align="center"|2005 6.5
2006 6.6
2007 6.7
2008 6.7
2009 6.8
2010 6.9
2011 7
2012 7
2013 7.1
2014 7.2
2015 7.3
2016 7.3
2017 7.4
2018 7.5
2019 7.6
2020 7.6
2021 7.7
2022 7.8
2023 7.9
2024 7.9
2025 8
2026 8.1
2027 8.2
2028 8.2
2029 8.3
2030 8.4
2031 8.5
2032 8.5
|align="center"|
|align="left"|
|-
|align="center"|U.S. Population Estimate (millions)
|align="center"|Equivalent to 310+3*(Year - 2010) million
|align="center"|2000 280
2001 283
2002 286
2003 289
2004 292
2005 295
2006 298
2007 301
2008 304
2009 307
2010 310
2011 313
2012 316
2013 319
2014 322
2015 325
2016 328
2017 331
2018 334
2019 337
2020 340
2021 343
2022 346
2023 349
2024 352
2025 355
2026 358
2027 361
2028 364
2029 367
2030 370
2031 373
2032 376
|align="center"|
|align="left"|
|-
|align="center"|Electron rest energy
|align="center"|e/716 Joules
|align="center"|8.17948276564429*10−14
|align="center"|8.18710438*10−14 (rounded)
|align="left"|
|-
|align="center"|Light-year(miles)
|align="center"|2(42.42)
|align="center"|5884267614436.97 (rounded)
|align="center"|9460730472580800 (meters in a light-year, by definition) / 1609.344 (meters in a mile) = 8212439646337500/1397 (exact) = 5878625373183.61 (rounded)
|align="left"|{{w|42 (number)|42}} is, according to Douglas Adams' ''The Hitchhiker's Guide to the Galaxy'', the Answer to the Ultimate Question of Life, the Universe, and Everything.
|-
|align="center"|sin(60°) = √3/2
|align="center"|e/π
|align="center"|0.8652559794 (rounded)
|align="center"|0.8660254038 (rounded)
|align="left"|
|-
|align="center"|√3
|align="center"|2e/π
|align="center"|1.7305119589 (rounded)
|align="center"|1.7320508076 (rounded)
|align="left"|
|-
|align="center"|gamma(Euler's gamma constant)
|align="center"|1/√3
|align="center"|0.5773502692 (rounded)
|align="center"|0.5772156649015328606065120900824024310421...
|align="left"|In {{w|mathematics}}, the {{w|Euler-Mascheroni constant}} (Euler gamma constant) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.
|-
|align="center"|Feet in a meter
|align="center"|5/(e√π)
|align="center"|3.2815481951
|align="center"|1/.3048 (exact) = 3.280839895 (rounded)
|align="left"|
|-
|align="center"|√5
|align="center"|2/e + 3/2
|align="center"|2.2357588823 (rounded)
|align="center"|2.2360679775 (rounded)
|align="left"|
|-
|align="center"|Avogadro's number
|align="center"|69π√5
|align="center"|6.02191201246329*1023 (rounded)
|align="center"|6.02214129*1023 (rounded)
|align="left"|Also called a Mole for shorthand, this is (roughly) the number of individual atoms in twelve grams of pure Carbon. Used in basically every application of chemistry.
|-
|align="center"|Gravitational constant G
|align="center"|1 / e(pi - 1)(pi + 1)
|align="center"|6.67361106850561*10−11 (rounded)
|align="center"|6.67385*10−11 (rounded)
|align="left"|The universal {{w|gravitational constant}} G is equal to F*r2/Mm, where F is the gravitational force between two objects, r is the distance between them, and M and m are their masses.
|-
|align="center"|R(gas constant)
|align="center"|(e+1) √5
|align="center"|8.3143309279 (rounded)
|align="center"|8.3144622 (rounded)
|align="left"|The {{w|gas constant}} relates energy to temperature in physics, as well as a gas's volume, pressure, temperature and {{w|mole (unit)|molar amount}} (hence the name).
|-
|align="center"|Proton-electron mass ratio
|align="center"|6*π5
|align="center"|1836.1181087117 (rounded)
|align="center"|1836.15267246 (rounded)
|align="left"|
|-
|align="center"|Liters in a gallon (U.S. liquid gallon, defined by law as 231 cubic inches)
|align="center"|3 + π/4
|align="center"|3.7853981634 (rounded)
|align="center"|3.785411784 (exact)
|align="left"|
|-
|align="center"|''g''0 or ''g''n
|align="center"|6 + ln(45)
|align="center"|9.8066624898 (rounded)
|align="center"|9.80665 (standard)
|align="left"|Standard gravity, or standard acceleration due to free fall is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665 m/s2, which is exactly 35.30394 (km/h)/s (about 32.174 ft/s2, or 21.937 mph/s). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from rotation of the Earth (but which is small enough to be neglected for most purposes); the total (the apparent gravity) is about 0.5 percent greater at the poles than at the equator. Randall used a letter g without a suffix, which can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth.
|-
|align="center"|Proton-electron mass ratio
|align="center"|(e8 - 10) / ϕ
|align="center"|1836.1530151398 (rounded)
|align="center"|1836.15267246 (rounded)
|align="left"|ϕ is the {{w|golden ratio}}, or (1 + √5)/2. It has many interesting geometrical properties.
|-
|align="center"|Ruby laser wavelength
|align="center"|1 / (12002)
|align="center"|.00000069444444444444... (repeating decimal)
|align="center"|694.3 nm
|align="left"|The ruby laser wavelength varies because "ruby" is not clearly defined.
|-
|align="center"|Mean Earth Radius
|align="center"|(58)*6e
|align="center"|2343750e (exact), 6,370,973.035450887 (6370 km, 973 m, 3 cm, 5 mm, 450 μm, 887 nm, 270 pm, 375 fm, 673 am, 760 zm, 982 ym) (rounded)
|align="center"|6,371,008.7 (International Union of Geodesy and Geophysics definition)
|align="left"|The {{w|Earth radius#mean radii|mean earth radius}} varies because there is not one single way to make a sphere out of the earth. Randall's value lies within the actual variation of Earth's radius. The International Union of Geodesy and Geophysics (IUGG) defines the mean radius as 2/3 of the equatorial radius (6,378,137.0 m) plus 1/3 of the polar radius (6,356,752.3 m).
|-
|align="center"|√2
|align="center"|3/5 + π/(7-π)
|align="center"|1.4142200581 (rounded)
|align="center"|1.4142135624 (rounded)
|align="left"|There are reoccurring math jokes along the lines of, "3/5 + π/(7 – π) – √2 = 0, but your calculator is probably not good enough to compute this correctly".
|-
|align="center"|cos(π/7) + cos(3π/7) + cos(5π/7)
|align="center"|1/2
|align="center"|0.5
|align="center"|0.5 (exact)
|align="left"|This is the exactly correct equation referred to in the note, "Pro tip - Not all of these are wrong", as shown below and also [http://math.stackexchange.com/questions/140388/how-can-one-prove-cos-pi-7-cos3-pi-7-cos5-pi-7-1-2 here]. If you're still confused, the functions use {{w|radians}}, not {{w|degrees (angle)|degrees}}.
|-
|align="center"|γ(Euler's gamma constant)
|align="center"|e/34 + e/5
|align="center"|0.5772154006 (rounded)
|align="center"|0.5772156649015328606065120900824024310421...
|align="left"|In {{w|mathematics}}, the {{w|Euler-Mascheroni constant}} (Euler gamma constant) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.
|-
|align="center"|√5
|align="center"|(13 + 4π) / (24 - 4π)
|align="center"|2.2360678094 (rounded)
|align="center"|2.2360679775 (rounded)
|align="left"|
|-
|align="center"|Σ 1/nn
|align="center"|ln(3)e
|align="center"|1.2912987577 (rounded)
|align="center"|1.2912859971 (rounded)
|align="left"|
|}

===Proof===

One of the "approximations" actually is precisely correct: cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2. Here is a proof:

cos(π/7) + cos(3π/7) + cos(5π/7)

* Multiplying by 1 (or by a number divided by itself) leaves the equation unchanged.

= (cos(π/7) + cos(3π/7) + cos(5π/7)) (2sin(π/7)/(2sin(π/7)))

* The 2sin(π/7) on the top of the fraction is multiplied through the original equation.

= (2cos(π/7)sin(π/7) + 2cos(3π/7)sin(π/7) + 2cos(5π/7)sin(π/7))/(2sin(π/7))

* Use the trigonometric identity 2cos(A)sin(B)=sin(A+B)-sin(A-B) on the 2nd two terms ([2cos(3π/7)sin(π/7)] + {2cos(5π/7)sin(π/7)}) /(2sin(π/7))

= (2cos(π/7)sin(π/7) + [sin(3π/7+π/7) - sin(3π/7-π/7)] + {sin(5π/7+π/7) - sin(5π/7-π/7)}) (1/2sin(π/7)) 
= (2cos(π/7)sin(π/7) + [sin(4π/7) - sin(2π/7)] + {sin(6π/7) - sin(4π/7)})/(2sin(π/7))

* Use the trigonometric identity 2cos(A)sin(A) = sin(2A) on the first term (2cos(π/7)sin(π/7))

= (sin(2π/7) + [sin(4π/7) - sin(2π/7)] + {sin(6π/7) - sin(4π/7)}) (1/2sin(π/7)) 
= (sin(6π/7) + [sin(2π/7) - sin(2π/7)] + {sin(4π/7) - sin(4π/7)}) (1/2sin(π/7)) 
= (sin(6π/7))/(2sin(π/7))

* Note that 6π/7 = (7π - π)/7 = 7π/7 - π/7 = π - π/7.

= (sin(π - π/7))/(2sin(π/7))

*Since sines of supplementary angles are equal.

= (sin(π/7))/(2sin(π/7)) 
= (1/2) (sin(π/7)/sin(π/7)) 
= 1/2

==Transcript==
:'''A table of slightly wrong equations and identities useful for approximations and/or trolling teachers.'''
:(Found using a mix of trial-and-error, ''Mathematica'', and Robert Munafo's ''Ries'' tool.)
: All units are SI MKS unless otherwise noted.

:{| class="wikitable"
|-
|colspan="2" align="center" | Relation:
|align="center" | Accurate to within:
|-
|align="center" | One light year(m)
|align="center" | 998
|align="center" | one part in 40
|-
|align="center" | Earth Surface(m2)
|align="center" | 698
|align="center" | one part in 130
|-
|align="center" | Ocean's volume(m3)
|align="center" | 919
|align="center" | one part in 70
|-
|align="center" | Seconds in a year
|align="center" | 754
|align="center" | one part in 400
|-
|align="center" | Seconds in a year (rent method)
|align="center" | 525,600 x 60
|align="center" | one part in 1400
|-
|align="center" | Age of the universe (seconds)
|align="center" | 1515
|align="center" | one part in 70
|-
|align="center" | Planck's constant
|align="center" | 1/(30πe)
|align="center" | one part in 110
|-
|align="center" | Fine structure constant
|align="center" | 1/140
|align="center" | [I've had enough of this 137 crap]
|-
|align="center" | Fundamental charge
|align="center" | 3/(14 * πππ)
|align="center" | one part in 500
|-
|align="center"|White House Switchboard
|colspan="2" align="center"|1/ 
π√(e(1 + (e-1)√8))
|-
|align="center"|Jenny's Constant
|colspan="2" align="center"|(7(e/1 - 1/e) - 9) * π2
|-
|colspan="3" align="center"|Intermission: World Population Estimate which should stay current for a decade or two: 
Take the last two digits of the current year

Example: 20[14]

Subtract the number of leap years since hurricane Katrina

Example:14 (minus 2008 and 2012) is 12

Add a decimal point

Example: 1.2

Add 6

Example: 6 + 1.2

7.2 = World population in billions.

Version for US population:

Example: 20[14]

Subtract 10

Example: 4

Multiply by 3

Example: 12

Add 10

Example: 3[22] million
|-
|align="center"|Electron rest energy
|align="center"|e/716 Joules
|align="center"|one part in 1000
|-
|align="center"|Light-year(miles)
|align="center"|2(42.42)
|align="center"|one part in 1000
|-
|colspan="2" align="center"|sin(60°) = √3/2 = e/π
|align="center"|one part in 1000
|-
|colspan="2" align="center"|√3 = 2e/π
|align="center"|one part in 1000
|-
|align="center"|gamma(Euler's gamma constant)
|align="center"|1/√3
|align="center"|one part in 4000
|-
|align="center"|Feet in a meter
|align="center"|5/(e√π)
|align="center"|one part in 4000
|-
|colspan="2" align="center"|√5 = 2/e + 3/2
|align="center"|one part in 7000
|-
|align="center"|Avogadro's number
|align="center"|69π√5
|align="center"|one part in 25,000
|-
|align="center"|Gravitational constant G
|align="center"|1 / e(pi - 1)(pi + 1)
|align="center"|one part in 25,000
|-
|align="center"|R(gas constant)
|align="center"|(e+1) √5
|align="center"|one part in 50,000
|-
|align="center"|Proton-electron mass ratio
|align="center"|6*π5
|align="center"|one part in 50,000
|-
|align="center"|Liters in a gallon
|align="center"|3 + π/4
|align="center"|one part in 500,000
|-
|align="center"|g
|align="center"|6 + ln(45)
|align="center"|one part in 750,000
|-
|align="center"|Proton-electron mass ratio
|align="center"|(e8 - 10) / ϕ
|align="center"|one part in 5,000,000
|-
|align="center"|Ruby laser wavelength
|align="center"|1 / (12002)
|align="center"|[within actual variation]
|-
|align="center"|Mean Earth Radius
|align="center"|(58)*6e
|align="center"|[within actual variation]
|-
|colspan="3" align="center"|Protip - not all of these are wrong:
|-
|colspan="2" align="center"|√2 = 3/5 + π/(7-π)
|align="center"|cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2
|-
|align="center"|γ(Euler's gamma constant) = e/34 + e/5
|align="center"|√5 = (13 + 4π) / (24 - 4π)
|align="center"|Σ 1/nn = ln(3)e
|}

{{comic discussion}}
[[Category:Charts]]
[[Category:Math]]
[[Category:Physics]]
[[Category:Protip]]

1655: Doomsday Clock

2016-03-14T04:28:24Z

108.162.214.143: Blanked the page

Talk:259: Clichéd Exchanges

2015-10-31T22:45:25Z

108.162.214.143:

Is this correction satisfactory? Can I remove the tag? [[User:ImVeryAngryItsNotButter|ImVeryAngryItsNotButter]] ([[User talk:ImVeryAngryItsNotButter|talk]]) 00:54, 8 March 2014 (UTC)
:I removed it, because it looks good to me. [[Special:Contributions/108.162.250.219|108.162.250.219]] 13:32, 12 March 2014 (UTC)

I thought the cliche being referred to was "wrecked 'em? I hardly knew 'em!" (a double entendre on "rectum" ) http://ask.metafilter.com/122210/JokeFilter-What-is-the-origin-of-the-joke-with-the-punchline-rectum-damn-near-killed-him [[Special:Contributions/66.202.132.250|66.202.132.250]] 14:25, 5 April 2013 (UTC)
:In my experience it's a general "<tagword>, I hardly knew(/know) her(/him)", where the tagword is an -er/-im word and can (by sheer force of will, often groan-worthy) be taken as a double-entendre spawn. e.g. "Which cathedral is that in the picture?" "Chester." "Chester? I hardly know 'er!" (The worse the better, arguably, but that example's probably too flat.)
:Your form follows alongside of that. But this cliché is the mismatched follow-up, only sparked off (albeit by deliberate disassociation) by the "O RLY?" cliché as feed-line. [[Special:Contributions/178.98.31.27|178.98.31.27]] 10:30, 20 June 2013 (UTC)

The double entendre in this case is O RLY ~ orally? [[User:Undee|Undee]] ([[User talk:Undee|talk]]) 11:24, 18 October 2013 (UTC)

I never thought of it as a double entendre- I thought it was a play on words of Irish names,(as evidenced by the ommision of the first letter in some words) i.e. O'reilly. In this case, it would be "O'reilly? I 'ardly know 'er!" {{unsigned ip|108.162.221.243}}

The fact that this is a collaborative wiki doesn't not mean you should put in every ludicrous and idiosyncratic interpretation that has special meaning to you and clearly has nothing to do with what Randall, or people in the rest of the world, understood the comic to be. O RLY is not a reference to an Irish name, or a Hebrew name, or anything at all other than the eminently popular O RLY meme. Period. Leave your personal nonsense out of this wiki.

259: Clichéd Exchanges

2015-10-31T22:42:26Z

108.162.214.143: /* Explanation */

{{comic
| number = 259
| date = May 9, 2007
| title = Clichéd Exchanges
| image = cliched exchanges.png
| titletext = It's like they say, you gotta fight fire with clichés.
}}

==Explanation==
Another entry into the [[My Hobby]] series.

"{{w|O RLY?}}" is an Internet meme typically used to express sarcastic agreement with or feigned surprise at a statement. The typical response to "O RLY" is usually "YA RLY", "NO WAI" or "SRSLY?" These exchanges are SMS abbreviations for "Oh really?", "Yeah really", "No way!", and "Seriously?" respectively.

However, [[Cueball]]'s response avoids this typical exchange, instead replying with another cliché, derived from a classic double entendre.

In this cliché, the speaker responds to a statement containing a word ending with '-er', and turns it into a sexual reference. The setup is as follows:

: '''Alan:''' ''"Do you want to come over to my house? My wife and I are playing poker."''
: '''Bob:''' ''"Poker? I hardly KNOW her!"''

Such a double entendre makes no sense in the context of an O RLY exchange. In the case of the comic, the non-sequitur will likely baffle the person on the left and derail the conversation, to the amusement of the person on the right. The reason [[Randall]] makes this a hobby is, presumably, that it bores him when people fall back on clichés for comedy, and he seeks inventive ways to humor himself in these situations. ''See, for example'', https://xkcd.com/16/.

The title text takes the real cliché "fight fire with fire," and combines it with the more literal "fight clichés with clichés." The resulting statement follows a very similar principle to the situation in the comic proper.

==Transcript==
:My Hobby:
:Derailing clichéd exchanges by using the wrong replies

:Friend: O RLY?
:Cueball: O RLY? I 'ardly know 'er!

{{comic discussion}}
[[Category:My Hobby]]
[[Category:Comics featuring Cueball]]

259: Clichéd Exchanges

2015-10-31T22:41:46Z

108.162.214.143: /* Explanation */

{{comic
| number = 259
| date = May 9, 2007
| title = Clichéd Exchanges
| image = cliched exchanges.png
| titletext = It's like they say, you gotta fight fire with clichés.
}}

==Explanation==
Another entry into the [[My Hobby]] series.

"{{w|O RLY?}}" is an Internet meme typically used to express sarcastic agreement with or feigned surprise at a statement. The typical response to "O RLY" is usually "YA RLY", "NO WAI" or "SRSLY?" These exchanges are SMS abbreviations for "Oh really?", "Yeah really", "No way!", and "Seriously?" respectively.

However, [[Cueball]]'s response avoids this typical exchange, instead replying with another cliché, derived from a classic double entendre.

In this cliché, the speaker responds to a statement containing a word ending with '-er', and turns it into a sexual reference. The setup is as follows:

: '''Alan:''' ''"Do you want to come over to my house? My wife and I are playing poker."''
: '''Bob:''' ''"Poker? I hardly KNOW her!"''

Such a double entendre makes no sense in the context of an O RLY exchange. In the case of the comic, the non-sequitur will likely baffle the person on the left and derail the conversation, to the amusement of the person on the right. The reason [[Randall]] makes this a hobby is, presumably, that it bores him when people fall back on clichés for comedy, and he seeks inventive ways to humor himself in these situations. ''See'''', for example'', https://xkcd.com/16/.

The title text takes the real cliché "fight fire with fire," and combines it with the more literal "fight clichés with clichés." The resulting statement follows a very similar principle to the situation in the comic proper.

==Transcript==
:My Hobby:
:Derailing clichéd exchanges by using the wrong replies

:Friend: O RLY?
:Cueball: O RLY? I 'ardly know 'er!

{{comic discussion}}
[[Category:My Hobby]]
[[Category:Comics featuring Cueball]]

549: Westley's a Dick

2015-06-16T17:27:33Z

108.162.214.143: /* Explanation */

{{comic
| number =549
| date =February 27, 2009
| title =Westley's a Dick
| image =westleys_a_dick.png
| titletext =Inigo/Buttercup 4eva <3
}}

==Explanation==
{{incomplete|Clean up or remove movie synopsis}}
This is an alternate take on the 1973 fantasy romance novel ''{{w|The Princess Bride}}'' written by {{w|William Goldman}} which became a {{w|The Princess Bride (film)|film in 1987}}.

In the movie the main character, Buttercup, believes she has lost her first love to the Dread Pirate Roberts years ago. In the present she is considered one of the most beautiful women of the land and so is being married off to a Prince. To provoke a war she has been kidnapped by mercenaries one of which is a very honorable Spanish swordsman named Inigo Montoya. A man claiming to be the the Dread Pirate Roberts rescues her. She attacks him pulling him down a hill. While tumbling down the hill he shouts back "as you wish" identifying him as her first love.

There are, however, several "dick moves" Westley must have made in order for the film's narrative to make sense.
# He took over as the Dread Pirate Roberts becoming a pirate and therefore not respectable, killing people, sacking ports, and looting ships for a living.
# Over the last five years, Westley has allowed Buttercup to believe that he'd been murdered, preventing her getting on with the rest of her life.

Westly breaks the fourth wall and claims he did all of these things for the sake of the {{w|narrative}}. In other words he did it to make the story better.
In the comic Buttercup realizes that Westley has behaved like a dick and chooses to give her love to Inigo Montoya. But in the movie, he and Buttercup end up together in spite of this behavior!

The title text shows what looks like a message she and Inigo has written together, for instance in a heart on a tree. Inigo is the Spaniard referred to by Buttercup. Their names, then forever (4eva) and a heart (smiley heart = "<3"), Implying they did end up together according to this version of the story.

It is not the first time [[Randall]] has referenced this movie, as the Dread Pirate was referenced in [[345: 1337: Part 5]], and a quote from this movie is in the title text of [[1427: iOS Keyboard]]. So it seems like a film that has some meaning for Randall.

===Princess Bride ===
The story takes place in the country of Florin. Buttercup (played by {{w|Robin Wright}} and here depicted as a girl with long hair) was a farmer who took her greatest joy from bossing Westley ({{w|Cary Elwes}} here depicted as [[Cueball]] with a black {{w|bandana}}) around like a servant. His only reply to her requests would be, "As you wish". As time passed, Buttercup realized that when Westley said "As you wish", what he really meant was "I love you". And one day she realized that she truly loved him back.

However, having no money for marriage, Westley went away to seek his fortune across the sea. Buttercup soon received word that Westley had been murdered by the {{w|Dread Pirate Roberts}}, and for days she neither slept nor ate, falling into a deep despondency and swearing that she would never love again. But really Westly was apprenticing under the Dread Pirate Roberts. Later taking over the title from am man who ''also'' isn't the original DPR. Westley became, at minimum, the fourth man known as the Dread Pirate Roberts — it's a legacy name designed to evoke fear into the populace. (As he said, no one would surrender to the Dread Pirate ''Westley''.)

Five years later, the aged King of Florin is near death, and the heir apparent, Prince Humperdinck, chooses Buttercup to be his bride, considering her to be the fairest maiden in the land. However, Buttercup doesn't love him. One day, while out riding, she is captured by three bandits — a Sicilian self-proclaimed genius named Vizzini, Spanish swordsman Inigo Montoya, and gentle giant Fezzik. (Vizzini is the only one of the trio who's genuinely malevolent, though.) The trio had been hired by Humperdinck to kill Buttercup and make it look like rival nation Guilder was responsible, giving Humperdinck the only excuse he needs to start a war between the two countries.

What they didn't count on was that Westley, wearing the outfit of a "Man in Black" (all-black clothing, sword, and black mask) was following them to stop them. Catching up to the trio, Westley defeats Inigo in fencing, Fezzik in hand-to-hand combat (rendering the two of them unconscious), and then kills Vizzini in a battle of wits.

Westley doesn't reveal his identity to Buttercup at first, but he gladly admits to being the Dread Pirate Roberts. Believing him to have been responsible for Westley's death, Buttercup gets into a vehement argument with him, culminating with her saying, "I ''died'' that day! And you can die too, for all I care!" She pushes him off a hill, with Westley replying "Aaaaaass... yoooooouuuu... wiiiiiish!" on the way down. Finally realizing who he is, she rolls down after him.

Of course, Inigo has had to be a bad guy for awhile now himself, but he admitted even to Westley that he was just doing it to pay the bills.

===Inigo Montoya===
Inigo's father was commissioned to make a sword for a nobleman with a six-fingered right hand. When the payment was to be made the six-fingered man tried to lower the price. He refused to sell the six-fingered man the sword as he felt the six-fingered man could not appreciate the sword. The six-fingered man killed Inigo's father in front of Inigo. Inigo challenged the six-fingered man to a fight and promptly lost. The six-fingered mans spared Inigo's life and allowed him to keep the sword, but marks his face with two cuts, one on each cheek. Afterwords Inigo devoted himself to becoming a great swordsman to avenge his father.

After his training was complete he was unable to find the six-fingered man. Inigo becomes a drunk and he joins a group of mercenaries lead by Vizzini. Vizzini, Inigo, and a Turk named Fezzik are hired by an unknown man to kidnap and kill the "princess bride", Buttercup. While rescuing Buttercup, Westley defeats Inigo, but spares his life. Inigo falls back into drunkenness. Eventually, Fezzik finds him and helps him regain his health. They rescue Westley after discovering he was captured by the six-fingered man. Inigo joins Westley to fight Humperdinck and find the six-fingered man.

While storming Humperdinck's castle, Inigo confronts the six-fingered man reciting the words he has practiced for this day since he was a child: "Hello. My name is Inigo Montoya. You killed my father. Prepare to die." He chases the six-fingered man until the six-fingered man throws a knife, delivering what would be a mortal wound to any lesser man. Mocking Inigo's quest as the six-fingered prepares to deliver the fatal blow. At the last second, Inigo recovers his strength by repeating his montra "Hello. My name is Inigo Montoya. You killed my father. Prepare to die." Inigo and duels the six-fingered man continuously repeating the fateful words. Inigo disarms marks the face of the six-fingered man, as the six-fingered man had done to him. After the six-fingered man begs for his life and offering to give Inigo anything the six-fingered man attacks again. Inigo replies, "I want my father back, you son of a bitch," and kills him.

At the end of the film, having avenged his father and thus no longer in "the revenge business," Inigo ponders what he will do with the rest of his life. In response, Westley offers Inigo the position of his successor as "The Dread Pirate Roberts." The novel ends with Inigo's wounds reopening while he is on the run from the Brute Squad, leaving his future in doubt.

==Transcript==
:[A girl (Buttercup) with long hair and a man (Westley) looking like Cueball but with a bandana lies at the foot of a high cliff. There is a forest in the background]
:Buttercup: Oh, my sweet Westley!

:[Buttercup sits on her knees, Westley takes off his bandana.]
:Buttercup: Why did you let me think you were dead?
:Westley: You shacked up with the prince!
:Buttercup: After years of mourning! The worst pain of my life!

:[Buttercup stands up looking down on Westley who still sits with the bandana in his hand.]
:Buttercup: And now you ... kill people?
:Westley: I'd hardly be a dread pirate if I didn't.
:Buttercup: How lovable.

:[Westley stands with the bandana in hand while Buttercup walks away from him.]

:Westley: It was for the sake of the narrative!
:Buttercup: Fuck the narrative. I'm going to go see if that Spaniard's single.
:Westley: ...As you wish.

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Romance]]