Fungrim entry: 47acde

Table of simple expressions involving

\pi

to 50 digits

$x$	$x \; (\text{nearest } 50 \text{D})$
$\pi$	3.1415926535897932384626433832795028841971693993751
$2 \pi$	6.2831853071795864769252867665590057683943387987502
$3 \pi$	9.4247779607693797153879301498385086525915081981253
$4 \pi$	12.566370614359172953850573533118011536788677597500
$\frac{\pi}{2}$	1.5707963267948966192313216916397514420985846996876
$\frac{3 \pi}{2}$	4.7123889803846898576939650749192543262957540990627
$\frac{\pi}{3}$	1.0471975511965977461542144610931676280657231331250
$\frac{2 \pi}{3}$	2.0943951023931954923084289221863352561314462662501
$\frac{\pi}{4}$	0.78539816339744830961566084581987572104929234984378
$\frac{3 \pi}{4}$	2.3561944901923449288469825374596271631478770495313
$\frac{\pi}{5}$	0.62831853071795864769252867665590057683943387987502
$\frac{2 \pi}{5}$	1.2566370614359172953850573533118011536788677597500
$\frac{3 \pi}{5}$	1.8849555921538759430775860299677017305183016396251
$\frac{4 \pi}{5}$	2.5132741228718345907701147066236023073577355195001
$\frac{\pi}{6}$	0.52359877559829887307710723054658381403286156656252
$\frac{5 \pi}{6}$	2.6179938779914943653855361527329190701643078328126
$\frac{1}{\pi}$	0.31830988618379067153776752674502872406891929148091
$\frac{2}{\pi}$	0.63661977236758134307553505349005744813783858296183
$\frac{1}{2 \pi}$	0.15915494309189533576888376337251436203445964574046
${\pi}^{2}$	9.8696044010893586188344909998761511353136994072408
${\left(2 \pi\right)}^{2}$	39.478417604357434475337963999504604541254797628963
$\frac{{\pi}^{2}}{2}$	4.9348022005446793094172454999380755676568497036204
$\frac{{\pi}^{2}}{4}$	2.4674011002723396547086227499690377838284248518102
$\frac{{\pi}^{2}}{6}$	1.6449340668482264364724151666460251892189499012068
$\frac{1}{{\pi}^{2}}$	0.10132118364233777144387946320972763890435877467225
$\frac{1}{{\left(2 \pi\right)}^{2}}$	0.025330295910584442860969865802431909726089693668062
${\pi}^{3}$	31.006276680299820175476315067101395202225288565885
${\pi}^{4}$	97.409091034002437236440332688705111249727585672685
$\sqrt{\pi}$	1.7724538509055160272981674833411451827975494561224
$\sqrt{2 \pi}$	2.5066282746310005024157652848110452530069867406099
$\frac{1}{\sqrt{\pi}}$	0.56418958354775628694807945156077258584405062932900
$\frac{1}{\sqrt{2 \pi}}$	0.39894228040143267793994605993438186847585863116493
$\log(\pi)$	1.1447298858494001741434273513530587116472948129153
$\log\!\left(2 \pi\right)$	1.8378770664093454835606594728112352797227949472756
$\frac{1}{2} \log\!\left(2 \pi\right)$	0.91893853320467274178032973640561763986139747363778
${e}^{\pi}$	23.140692632779269005729086367948547380266106242600
${e}^{\pi / 2}$	4.8104773809653516554730356667038331263901708746645
${e}^{2 \pi}$	535.49165552476473650304932958904718147780579760329
${e}^{-\pi}$	0.043213918263772249774417737171728011275728109810633
${e}^{-\pi / 2}$	0.20787957635076190854695561983497877003387784163177
${e}^{-2 \pi}$	0.0018674427317079888144302129348270303934228050024753
${e}^{\pi} - \pi$	19.999099979189475767266442984669044496068936843225

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`Pow`	${a}^{b}$	Power
`Sqrt`	$\sqrt{z}$	Principal square root
`Log`	$\log(z)$	Natural logarithm
`Exp`	${e}^{z}$	Exponential function

Source code for this entry:

Entry(ID("47acde"),
    Description("Table of simple expressions involving", Pi, "to 50 digits"),
    Table(Var(x), TableValueHeadings(x, NearestDecimal(x, 50)), TableSplit(1), List(Tuple(Pi, Decimal("3.1415926535897932384626433832795028841971693993751")), Tuple(Mul(2, Pi), Decimal("6.2831853071795864769252867665590057683943387987502")), Tuple(Mul(3, Pi), Decimal("9.4247779607693797153879301498385086525915081981253")), Tuple(Mul(4, Pi), Decimal("12.566370614359172953850573533118011536788677597500")), Tuple(Div(Pi, 2), Decimal("1.5707963267948966192313216916397514420985846996876")), Tuple(Div(Mul(3, Pi), 2), Decimal("4.7123889803846898576939650749192543262957540990627")), Tuple(Div(Pi, 3), Decimal("1.0471975511965977461542144610931676280657231331250")), Tuple(Div(Mul(2, Pi), 3), Decimal("2.0943951023931954923084289221863352561314462662501")), Tuple(Div(Pi, 4), Decimal("0.78539816339744830961566084581987572104929234984378")), Tuple(Div(Mul(3, Pi), 4), Decimal("2.3561944901923449288469825374596271631478770495313")), Tuple(Div(Pi, 5), Decimal("0.62831853071795864769252867665590057683943387987502")), Tuple(Div(Mul(2, Pi), 5), Decimal("1.2566370614359172953850573533118011536788677597500")), Tuple(Div(Mul(3, Pi), 5), Decimal("1.8849555921538759430775860299677017305183016396251")), Tuple(Div(Mul(4, Pi), 5), Decimal("2.5132741228718345907701147066236023073577355195001")), Tuple(Div(Pi, 6), Decimal("0.52359877559829887307710723054658381403286156656252")), Tuple(Div(Mul(5, Pi), 6), Decimal("2.6179938779914943653855361527329190701643078328126")), Tuple(Div(1, Pi), Decimal("0.31830988618379067153776752674502872406891929148091")), Tuple(Div(2, Pi), Decimal("0.63661977236758134307553505349005744813783858296183")), Tuple(Div(1, Mul(2, Pi)), Decimal("0.15915494309189533576888376337251436203445964574046")), Tuple(Pow(Pi, 2), Decimal("9.8696044010893586188344909998761511353136994072408")), Tuple(Pow(Mul(2, Pi), 2), Decimal("39.478417604357434475337963999504604541254797628963")), Tuple(Div(Pow(Pi, 2), 2), Decimal("4.9348022005446793094172454999380755676568497036204")), Tuple(Div(Pow(Pi, 2), 4), Decimal("2.4674011002723396547086227499690377838284248518102")), Tuple(Div(Pow(Pi, 2), 6), Decimal("1.6449340668482264364724151666460251892189499012068")), Tuple(Div(1, Pow(Pi, 2)), Decimal("0.10132118364233777144387946320972763890435877467225")), Tuple(Div(1, Pow(Mul(2, Pi), 2)), Decimal("0.025330295910584442860969865802431909726089693668062")), Tuple(Pow(Pi, 3), Decimal("31.006276680299820175476315067101395202225288565885")), Tuple(Pow(Pi, 4), Decimal("97.409091034002437236440332688705111249727585672685")), Tuple(Sqrt(Pi), Decimal("1.7724538509055160272981674833411451827975494561224")), Tuple(Sqrt(Mul(2, Pi)), Decimal("2.5066282746310005024157652848110452530069867406099")), Tuple(Div(1, Sqrt(Pi)), Decimal("0.56418958354775628694807945156077258584405062932900")), Tuple(Div(1, Sqrt(Mul(2, Pi))), Decimal("0.39894228040143267793994605993438186847585863116493")), Tuple(Log(Pi), Decimal("1.1447298858494001741434273513530587116472948129153")), Tuple(Log(Mul(2, Pi)), Decimal("1.8378770664093454835606594728112352797227949472756")), Tuple(Mul(Div(1, 2), Log(Mul(2, Pi))), Decimal("0.91893853320467274178032973640561763986139747363778")), Tuple(Exp(Pi), Decimal("23.140692632779269005729086367948547380266106242600")), Tuple(Exp(Div(Pi, 2)), Decimal("4.8104773809653516554730356667038331263901708746645")), Tuple(Exp(Mul(2, Pi)), Decimal("535.49165552476473650304932958904718147780579760329")), Tuple(Exp(Neg(Pi)), Decimal("0.043213918263772249774417737171728011275728109810633")), Tuple(Exp(Neg(Div(Pi, 2))), Decimal("0.20787957635076190854695561983497877003387784163177")), Tuple(Exp(Neg(Mul(2, Pi))), Decimal("0.0018674427317079888144302129348270303934228050024753")), Tuple(Sub(Exp(Pi), Pi), Decimal("19.999099979189475767266442984669044496068936843225")))))

Fungrim entry: 47acde

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