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#51 Re: This is Cool » A New Way Of Finding If "p" Is Composite. » 2016-04-23 01:08:13
It doesn't matter.
#52 Re: This is Cool » A New Way Of Finding If "p" Is Composite. » 2016-04-23 00:00:04
Let's try a little exercise:
#53 Re: This is Cool » A New Way Of Finding If "p" Is Composite. » 2016-04-22 22:08:08
Oh well, never mind.
#54 Euler Avenue » The isometry group of the plane » 2016-04-22 14:36:50
- Nehushtan
- Replies: 0
So what possible transformations are isometries of the plane? You might think that there were a whole bunch of them: rotations, reflections, and translations. (A reflection followed by a translation is sometimes called a glide reflection.) In fact the picture is simpler than that: it turns out that rotations and translations can be built up from reflections alone! A translation in a certain direction is simply a reflection in two axes perpendicular that direction, while a rotation about a point O is a reflection in two axes through O.
Hence any translation is a reflection in two axes perpendicular to the direction of translation whose distance apart is half the distance to be translated.[list=*]
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Hence any rotation is a reflection in two axes through the centre of rotation whose angular separation is half the angle to be rotated through.
#55 Re: Help Me ! » sid's new year resolution » 2016-04-21 19:42:42
The number of days he goes for at least one of the activities is
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so the number of days he goes for none of them is 366 minus that.
#56 Re: Euler Avenue » Algebraic topology » 2016-04-21 00:18:07
5. HAM-SANDWICH THEOREM
It is always possible to slice a three-layered ham sandwich with a single cut of a knife in such a way that each layer of the sandwich is divided into two exactly equal halves by the cut.
The ham-sandwich theorem can be proved using the Borsuk–Ulam theorem.
#58 Re: Puzzles and Games » Arrange Mathematical Operation Using 0-9 to Match the Post Number » 2016-04-20 18:50:28
#59 Re: Euler Avenue » Algebraic topology » 2016-04-20 11:09:01
4. BORSUK–ULAM THEOREM
#60 Re: Help Me ! » Hard math problem - ratios. » 2016-04-19 21:47:46
Have you made a typo somewhere?
#61 Re: Euler Avenue » What had you learned today that you found interesting? » 2016-04-19 09:57:33
I learn that it is possible to make a tetradecahedron with just regular hexagons and squares.
It is also possible to make a truncated icosahedron with regular pentagons and hexagons.
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#62 Re: Puzzles and Games » Can you suggest six names of great mathematicians quickly? » 2016-04-09 22:49:38
Euclid
Euler
Abel
Galois
Cantor
Poincaré
#63 Re: Help Me ! » Find all polynomials with integral coefficients satisfying » 2016-04-09 21:42:43
#64 Re: Puzzles and Games » Arrange Mathematical Operation Using 0-9 to Match the Post Number » 2016-03-26 03:59:13
#65 Re: Puzzles and Games » Arrange Mathematical Operation Using 0-9 to Match the Post Number » 2016-03-21 00:39:48
#66 Re: Help Me ! » Find all distinct subgroups of <32> in <Z60, +60> » 2016-03-16 07:24:59
My answer is <0>, <12>, <20>, <32>
Is this correct?
Looks good to me. As a subgroup of the given group, <32> = <4> is cyclic of order 15, and a cyclic group of order 15 has precisely four subgroups.
#67 Re: This is Cool » Mersenne Prime Theorem » 2016-03-16 05:11:36
, all possible prime factors will = where n= prime and m=any multiple..........
This is just another way of stating Fermat's little theorem, nothing new.
The statement is clearly true for n = 2.
If n is an odd prime then
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#68 Re: Help Me ! » Find all distinct subgroups of <32> in <Z60, +60> » 2016-03-16 04:57:48
Why does Bob Bundy always ask silly questions? 
#69 Re: Puzzles and Games » Arrange Mathematical Operation Using 0-9 to Match the Post Number » 2016-03-11 23:19:17
#70 Re: Help Me ! » Simultaneous equation » 2016-03-09 05:10:31
There are no solutions. Multiplying both equations together gives
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but neither satsifies either of the original equations.
#72 Re: Help Me ! » Math Problems » 2016-03-07 19:08:27
Let
be a function such that for x > 1. In that domain, f(x) has the form where a,b,c,d are integers and a,b are relatively prime. Find a+b+c+d.
The best I can do is as follows.
Now try three other values for f(x) and get three similar equations, which will enable you to solve for the four unknowns.
Since we are only interested in the sum of the unknowns, not their individual values, I doubt if this method is really efficient; nevertheless it's the best I can think of.