- #1
kingwinner
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1) We know that if [itex]\theta[/itex] is trisectible (with straightedge and compass), then [itex]\theta[/itex]/3 is constructible.
But is it also true that if [itex]\theta[/itex]/3 is constructible, then [itex]\theta[/itex] is trisectible (with straightedge and compass)?
If so, then I can say that since 15o is constructible, we have that 45 o is trisectible, right? (because we can copy an angle of 15o three times, thus trisecting the angle 45 o)
2) Let m,n be integers.
Then m|3n3 => m|n
and n|28n3 => n|m
I spent half an hour thinking about this, but I still have no clue...
Why are the implications (=>) true? Can someone please explain?
3) How can I prove that the acute angle whose cosine is 1/10 is constructible?
I know that if [itex]\theta[/itex] is constructible, then cos[itex]\theta[/itex] is constructible. But is the converse true? Why or why not?
Any help is appreciated!
But is it also true that if [itex]\theta[/itex]/3 is constructible, then [itex]\theta[/itex] is trisectible (with straightedge and compass)?
If so, then I can say that since 15o is constructible, we have that 45 o is trisectible, right? (because we can copy an angle of 15o three times, thus trisecting the angle 45 o)
2) Let m,n be integers.
Then m|3n3 => m|n
and n|28n3 => n|m
I spent half an hour thinking about this, but I still have no clue...
Why are the implications (=>) true? Can someone please explain?
3) How can I prove that the acute angle whose cosine is 1/10 is constructible?
I know that if [itex]\theta[/itex] is constructible, then cos[itex]\theta[/itex] is constructible. But is the converse true? Why or why not?
Any help is appreciated!
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