A Universe of Numbers. [Join Any Time]

[Ircher]

Ircher decided that the universe could use a number. He applied the secret power of base conversion to form the next number.

17

(in decimal) converted to octal =

21

[StrangerCoug]

After Jake ate the keleven, Coug realized that he was hungry, too, so he got a little carried away and made a square pi.

pi

^

2

=

pi^2

(Coug, if you want, you can edit your prev. message to add 11, or ask me how you want it made.)

(Done.)

[Jake The Wolfie]

100

/

5

=

20

[StrangerCoug]

Among the Greek letters that existed, there were pi and tau. Now there would be zeta(2), though that being a function with a number Coug had already created as a sole argument, he couldn't directly use the function. However, he knew what the function would output:

pi^2

/

6

=

pi^2/6

[Ircher]

Fun Fact: You can construct any square root of a rational length using just a compass and a straightedge. Speaking of square roots...

sqrt(

15

) =

sqrt(15)

[Jake The Wolfie]

So would this require 4 compasses and 4 straightedges?

sqrt(

sqrt(15)

) =

sqrt(sqrt(15))

[Ircher]

No, it would only require one compass and one straightedge. You would just have to do the process twice.

sqrt(

sqrt(sqrt(15))

=

sqrt(sqrt(sqrt(15)))

(Because why not?)

[Jake The Wolfie]

sqrt(sqrt(sqrt(15)))

^

3

=

(sqrt(sqrt(sqrt(15))))^3

[StrangerCoug]

"Square roots of square roots?" Coug asked. He saw that, by simplification, the square root of the square root was the fourth root, and the square root of the square root of the square root was the eighth root. But why did the root have to be a power of two? Odd roots had the power that taking one of a negative real number gave another negative real number.

cbrt(

-3

) =

-cbrt(3)

[D3f3nd3r]

With ten and e already here as the two most common bases for logarithms, D3f set out to use the third most common base for a logarithm instead.

lg(

10

) =

lg(10)

(log base-2)

Somewhere in the distance, a computer scientist cried out in joy.

[StrangerCoug]

(That's actually the common log of 10. A valid number, but not the base of the binary log xD)

Complex conjugate of (

255.75+i

) =

255.75-i

[Jake The Wolfie]

255.75-i

+

i

=

255.75

[D3f3nd3r]

"Lg" is the common log?

Idk I'm an engineer, so "log" is common and "ln" is natural

255.75-i

-

i

=

255.75-2i

[Jake The Wolfie]

(

255.75-2i

)^

2

=

65404.0625-1023i

[StrangerCoug]

"Lg" is the common log?

Idk I'm an engineer, so "log" is common and "ln" is natural

(Just plain "log" is ambiguous and depends on the context you're talking about. That's why the symbol lg (without the o) was devised.)

Im(

65404.0625-1023i

) =

1023

[Ircher]

For computer scientists, log always indicates the base-2 log. That allows us to say things like binary search is O(log(N)). So yeah, log depends on context and who you are talking to.

1023

+

1

=

1024

[Jake The Wolfie]

1024

x

i

=

1024i

[Sirius9121]

From the darkness, a pokemon, Growlithe, is born

[Sirius9121]

Ah, e and pi. Hmm

pi

+

e

=

pi+e (5.85987448205)

'True pie', said the Growlithe

[Jake The Wolfie]

1024

+

1024i

=

1024+1024i

[StrangerCoug]

Modulus of

1024+1024i

=

1024*sqrt(2)

[Sirius9121]

1024*sqrt(2)

^

2

=

2097152

[StrangerCoug]

(You technically need the parentheses around my entire number before squaring it or it'll be 2048, but I get you.)

log_

2

(

2097152

) =

21

[Sirius9121]

128

+

2

=

130

(i need this)

[StrangerCoug]

Who would have known that an imaginary number to the power of an imaginary number would be a real number?

i

^

i

=

e^(-pi/2)