nice stuff.
i must admit, i have a fondness for the simplicity of the semi-circle
(_1) as the unit of angle. No need for all that (usually) pointless
messing about with pi.
eg. if [c] is an angle measured in terms of a semicircle
then
]'x y' =. +. _1^ c =. %3 NB.
NB. 0.5 0.866025403784
On 2011-07-15 09:21, Bo Jacoby wrote:
>
>
> "We'll sample a sine wave at 194.18 Hz over 1 second" does not mean that "our
> x axis covers 194.18 radians". It means that our x axis covers 1220 radians.
>
> 194.18*2p1
> 1220.06892
>
> The trigonometric function ^0j2p1* can be written simply _1^+: (but alas
> not 1^ even if _1^2 is equal to 1).
>
> If y is a rational number then _1^+:y is an algebraic number. The
> transcendental numbers e=.^1 and pi=.o.1 do not show.
>
>
>
>
>> ________________________________
>> Fra: David Ward Lambert<[email protected]>
>> Til: programming<[email protected]>
>> Sendt: 10:13 torsdag den 14. juli 2011
>> Emne: [Jprogramming] Tau =: 2p1
>>
>> This clip from a recent [email protected] letter begs for the
>> turn:
>>
>>
>> NB. We'll sample a sine wave at 194.18 Hz over 1 second.
>> NB. Or in other words: our x axis covers 194.18 radians,
>> NB. and we'll choose our 8000 sample points from that range:
>>
>> x =: (194.18 * 2p1) * (%~ i.) 8000
>>
>>
>>
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>>
>>
>>
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