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Check Machin-like formulas: Difference between revisions
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{{task}}
[[wp:Machin-like_formula|Machin-like formulas]] are useful for efficiently computing numerical approximations to Pi.
Verify the following Machin-like formulas are correct by calculating the value of '''tan'''(''right hand side)'' for each equation using exact arithmetic and showing they equal 1:▼
;Task:
▲Verify the following Machin-like formulas are correct by calculating the value of  l '''tan''' (''right hand side)'' for each equation using exact arithmetic and showing they equal '''1''':
: <math>{\pi\over4} = \arctan{1\over2} + \arctan{1\over3}</math>
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: <math>{\pi\over4} = 88 \arctan{1\over172} + 51 \arctan{1\over239} + 32 \arctan{1\over682} + 44 \arctan{1\over5357} + 68 \arctan{1\over12943}</math>
and confirm that the following formula is incorrect by showing '''tan''' (''right hand side)'' is ''not'' '''1''':
: <math>{\pi\over4} = 88 \arctan{1\over172} + 51 \arctan{1\over239} + 32 \arctan{1\over682} + 44 \arctan{1\over5357} + 68 \arctan{1\over12944}</math>
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: <math>\tan(-a) = -\tan(a)</math>
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You can store the equations in any convenient data structure, but for extra credit parse them from human-readable [[Check_Machin-like_formulas/text_equations|text input]].
Note that to formally prove the formula correct you would also have to show that ''<math>{-3 pi \over 4}</math> < right hand side < <math>{5 pi \over 4}</math>'' due to ''<math>\tan()</math>'' periodicity.
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=={{header|D}}==
This uses the module of the Arithmetic Rational Task.
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