ConwayLife.com

Posted: **February 15th, 2023, 9:55 pm**

e^0.5(1 + √2/2) = 2.3479753 (+0.00008004)

Posted: **February 16th, 2023, 12:44 am**

C_R_116 wrote: February 15th, 2023, 9:55 pm e^0.5(1 + √2/2) = 2.3479753 (+0.00008004)

Is your formula means e^(0.5*(1+sqrt(2)/2)) or (e^0.5)*(1+sqrt(2)/2)?

Posted: **February 16th, 2023, 7:52 am**

PHPBB12345 wrote: February 16th, 2023, 12:44 am
C_R_116 wrote: February 15th, 2023, 9:55 pm e^0.5(1 + √2/2) = 2.3479753 (+0.00008004)
Is your formula means e^(0.5*(1+sqrt(2)/2)) or (e^0.5)*(1+sqrt(2)/2)?

Numerical verification says former.

Posted: **February 16th, 2023, 8:40 am**

587/250 = 2.348 (+0.0000247)

Posted: **February 16th, 2023, 9:15 am**

14142135623 wrote: February 16th, 2023, 8:40 am 587/250 = 2.348 (+0.0000247)

6^(1/6)+1 = 2.34800615460 (+0.00000615460)

Posted: **February 16th, 2023, 12:07 pm**

PHPBB12345 wrote: April 12th, 2501, 8:35 am
14142135623 wrote: April 12th, 2501, 3:00 am 587/250 = 2.348 (+0.0000247)
6^(1/6)+1 = 2.34800615460 (+0.00000615460)

¹³√(π⁹+36122) ≈ 2.34800628554 (+0.0000001309465)
6 leading 0's... >:D

Posted: **February 16th, 2023, 12:14 pm**

-sin(5 radians) * √6 ≈ 2.34887517 (+0.000868889349)

Posted: **February 16th, 2023, 12:34 pm**

hotdogPi wrote: February 16th, 2023, 12:14 pm -sin(5 radians) * √6 ≈ 2.34887517 (+0.000868889349)

sqrt(5)+1/(9-e^(-2)) ≈ 2.34887540248 (+0.0000002275856)

Posted: **February 16th, 2023, 1:16 pm**

PHPBB12345 wrote: February 16th, 2023, 12:34 pm
hotdogPi wrote: February 16th, 2023, 12:14 pm -sin(5 radians) * √6 ≈ 2.34887517 (+0.000868889349)
sqrt(5)+1/(9-e^(-2)) ≈ 2.34887540248 (+0.0000002275856)

log(36.6) + (pi/4) ≈ 2.34887924879 (+0.000003846312)

Posted: **February 16th, 2023, 2:04 pm**

rutabaga wrote: February 16th, 2023, 1:16 pm2.34887924879 (+0.000003846312)

Code: Select all

deRLE=(lambda rle: __import__('functools').reduce(lambda a,c: (lambda r,p,a: ((lambda s: (r|((c=='o')*((1<<s)-1))<<p,p+s,''))(int(a)) if a else (r|(c=='o')<<p,p+1,'')) if c in 'bo' else (r,p,a+c))(*a),rle,(0,0,''))[0])

∑_{n=1}^{∞} (∑_{k=1}^{∞} ((deRLE('oo10boobbobbo')/2**20)**(n*k))) = (lambda n,d: (ln(n/(n-d))-Ψ_{n/d}^{0} (1))/ln(n/d))(602115,1048576) ≈ 2.34888188574 (+0.0000026369563) (where Ψ is the q-polygamma function :-)
Edit:

PHPBB12345 wrote: February 16th, 2023, 12:34 pmsqrt(5)+1/(9-e^(-2)) ≈ 2.34887540248 (+0.0000002275856)

If you wanted to golf here, you could use negation's precedence over exponentiation (when in its right operand) to reduce a bracket pair

Posted: **February 16th, 2023, 4:04 pm**

DroneBetter wrote: February 16th, 2023, 2:04 pm
Code: Select all
deRLE=(lambda rle: __import__('functools').reduce(lambda a,c: (lambda r,p,a: ((lambda s: (r|((c=='o')*((1<<s)-1))<<p,p+s,''))(int(a)) if a else (r|(c=='o')<<p,p+1,'')) if c in 'bo' else (r,p,a+c))(*a),rle,(0,0,''))[0])
∑_{n=1}^{∞} (∑_{k=1}^{∞} ((deRLE('oo10boobbobbo')/2**20)**(n*k))) = (lambda n,d: (ln(n/(n-d))-Ψ_{n/d}^{0} (1))/ln(n/d))(602115,1048576) ≈ 2.34889358949 (+0.0000026369563) (where Ψ is the q-polygamma function

Your formula result is 2.3488818857482087651576835116681812652...

Posted: **February 16th, 2023, 7:56 pm**

sqrt(sqrt(e) + sqrt(15)) ≈ 2.34983 (+0.00095).

Posted: **February 17th, 2023, 12:22 am**

squareroot12621 wrote: February 16th, 2023, 7:56 pm sqrt(sqrt(e) + sqrt(15)) ≈ 2.34983 (+0.00095).

47/20 = 2.35 (+0.00017)

Posted: **February 17th, 2023, 10:15 am**

PHPBB12345 wrote: February 17th, 2023, 12:22 am
squareroot12621 wrote: February 16th, 2023, 7:56 pm sqrt(sqrt(e) + sqrt(15)) ≈ 2.34983 (+0.00095).
47/20 = 2.35 (+0.00017)

cube root 13 = 2.35133468772... (+0.00133468772...)

Posted: **February 17th, 2023, 10:26 am**

2.35140625

Posted: **February 17th, 2023, 10:26 am**

AwesomeButt wrote: February 17th, 2023, 10:26 am 2.35140625

where did you get the number from

Posted: **February 17th, 2023, 10:48 am**

rutabaga wrote: February 17th, 2023, 10:26 am
AwesomeButt wrote: February 17th, 2023, 10:26 am 2.35140625
where did you get the number from

I assume 15,049/6,400.

1 + sqrt(11/6) ≈ 2.35401 (+0.00260).

Posted: **February 17th, 2023, 10:50 am**

113/48 = 2.35416̅ (+0.000160265894)

Posted: **February 17th, 2023, 10:55 am**

2 + 1/(e + 0.1) ≈ 2.35483 (+0.00066).

Posted: **February 17th, 2023, 11:35 am**

√(190)+π/2−13 = 2.35484508 (+0.00001896)

Posted: **February 17th, 2023, 2:55 pm**

May13 wrote: February 17th, 2023, 11:35 am √(190)+π/2−13 = 2.35484508 (+0.00001896)

3*e-29/5 ≈ 2.35484548538 (+0.000000406492)

Posted: **February 17th, 2023, 9:07 pm**

∛(√3 + √13×π) ≈ 2.35489994 (+0.00005446).

Posted: **February 18th, 2023, 12:30 am**

squareroot12621 wrote: February 17th, 2023, 9:07 pm ∛(√3 + √13×π) ≈ 2.35489994 (+0.00005446).

e^(∛(π/5)) ≈ 2.35490063105 (+0.000000687036)

Posted: **February 18th, 2023, 1:50 am**

PHPBB12345 wrote: February 18th, 2023, 12:30 am
squareroot12621 wrote: February 17th, 2023, 9:07 pm ∛(√3 + √13×π) ≈ 2.35489994 (+0.00005446).
e^(∛(π/5)) ≈ 2.35490063105 (+0.000000687036)

2.355 (+0.0001)

Posted: **February 18th, 2023, 4:07 am**

AwesomeButt wrote: February 18th, 2023, 1:50 am 2.355 (+0.0001)

ln(1564)-5 = 2.355001921105 (+0.000001921105)

ConwayLife.com

My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]

Re: My number is larger [GAME]