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### #1

Posted 07 March 2008 - 03:55 PM

Their values are

pi = 3.1415926536 ...

e = 2.718281828459 ...

1 = unity

i = sqrt[-1]

Arrange these numbers, using them once and only once, so that they equal 0

using only the operations +, ×, and exponentiation.

Use the spoiler, Luke.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #2

Posted 07 March 2008 - 05:03 PM

### #3

Posted 07 March 2008 - 05:10 PM

Four basic numbers from science and mathematics have the symbols pi, e, 1 and i.

Their values are

pi = 3.1415926536 ...

e = 2.718281828459 ...

1 = unity

i = sqrt[-1]

Arrange these numbers, using them once and only once, so that they equal 0

using only the operations +, ×, and exponentiation.

Use the spoiler, Luke.

Are we allowed to use functions ... like ceiling, floor, Int()??

### #4

Posted 07 March 2008 - 05:30 PM

Sorry ... just the ones listed.Are we allowed to use functions ... like ceiling, floor, Int()??

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #5

Posted 07 March 2008 - 05:44 PM

### #6

Posted 07 March 2008 - 11:24 PM

the special case is:

e

^{pi*i}+ 1 = 0

which comes from this:

e

^{pi*i}= -1

which comes from this:

e

^{theta*i}= cos(theta) + i*sin(theta)

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