@MrWho Just draw a circle with centre at the point the angle is formed. Then consider the ratio of the arc subtended by the angle and the circumference of the circle. Multiply this by 360 degrees and you get your angle. This is independent of the radius of the circle.
The gradian is a unit of plane angle, equivalent to 1⁄400 of a turn.
It is also known as gon, grad, or grade. One grad equals 9⁄10 of a degree or π⁄200 of a radian. In continental Europe, the French term centigrade was in use for one hundredth of a grad, and the term myriograde was in use for one ten-thousandth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.
== History ==
The unit originated in France as the grade, along with the metric system. Due to confusion with existing grad(e) units of northern Europe, the name...
What I don't get @MikeMiller and @BalarkaSen and @skullpatrol is why some real analysis homework will get 70 views, 5 answers and 10 upvotes, but that, a genuine not homework question gets little attention
I think I have an allergy for the math in wikipedia. They disfigure some facts in a sophisticated manner in the process of briefing the theories; usually hard to catch but doesn't fool the eyes of the one who studied the topic rigorously.
Even though not more popular than wiki, I much like mathworld in this business. They swiftly maintain the "whereof one cannot speak, thereon one must be silent" policy.
Jeez... I was chastised for answering a question in a similar (but I think better) way as someone else. I had started before they posted, and didn't see their post until I posted. Excuuuse me!
I deleted soon after I posted, when I read the other answer.
@robjohn why was this bumped? not a complaint (though I don't like trivial edits to bump questions), but I can't tell why it's up again now... nothing seems to have been edited
It is mentioned in the faq, but I did not know about possibility of using strikethrough in chat. I suppose that <s>strike</s> <s>strike</s> does not work in chat, although it does work on the main.
Let a function from the set $ \{ f \in C^1 (\mathbb{R},\mathbb{R}) \, ; \ f(0)=0 \}$ to the set $C(\mathbb{R},\mathbb{R})$ be defined by $f \mapsto f'$. Show that this function is a bijection
Any hints? I know I have to prove that the mapping is surjective and injective, but not exactly sure how to start >^.^>
here goes : define Aut_H(G) to the auts of G which fixes H pointwise (G is a group and H <= G). the main theorem is that if N <= H <= G and N is a char subgroup of H which is in turn a char subgroup of G then there is a left-exact sequence 1 --> Aut_H(G) --> Aut_N(G) --> Aut_N(H)
the auts stuffs are a mimicry of galois groups and the char subgroups are a mimicry of galois extensions.
@Karl i won't bother giving a proof if you believe what i claimed
no, no, i mean there is nothing more to the proof than to produce the last morphism.
@KarlKronenfeld yeah, essentially so
what d'you think of this? proof's pretty elementary, but i am curious that something like galois theory which is defined over fields (an abstract object with terribly many structure) can be also defined over groups -- an object with far fewer structures.
essentially the action of Aut stuffs over the groups are precisely some kind of galois action.
Hi all! Question: Could we define a space $\mathbb{R}^{n} \times \mathbb{R}^{n\times n}$ for which we may define some algebraic operations (is this term correct?), such as summation, multiplication, etc? I am thinking something like the set of complex numbers, $\mathbb{C}$... Please help!
FYI, @Khallil, it's a problem in additive combinatorics to count the number of elts in $A + A$. You can give it a go if you want, it's not that hard, but careful with your flow of thoughts.
@N3buchadnezzar I am talking about the hardback of course. But really there are problems with that book. For example, it defines the multiple integral in terms of the iterated integral instead of proving it from the usual definitions.
I thought that $\lfloor ... \rfloor$ denote the floor function and $\lceil ... \rceil$ denoted the ceiling function. Anyway, I've seen $[ ... ]$ denote the floor function more often than not.
Hm, if I have an equation system like: (x+y)^2 = something (x-y)^2= something else, is it OK to take square roots of both equations and solve the corresponding equation system, or should one be more careful?
Where should I look for spaces(?) of the form $\mathbb{R}^{n} \times\mathbb{R}^{n\times n}$? I am not sure where these things belong to... Could you give a hand? thanks!
I mean, surely (x+y)^2=a implies (x+y)= \pm sqrt(a), shouldn't one be able to apply this to the system of equations and afterwards check the solutipns?