Apr
17
comment Calculate the last digit of $3^{347}$
$$(3^5)^{69} *3^2 =3^{69} *3^2$$
Apr
3
comment How can a piece of A4 paper be folded in exactly three equal parts?
1) With this method one can fold a letter an arbitrary number of times (if one does not reach physical limits ). So if one wants to fold it in 5 equal parts one first folds it in $2^3=8$ equal parts and the folds along the line through the top corner and the 5th mark. 2) One must use the second dimensions. When folding only parallel to one side one cannot fold into 3 equal parts. It is not possible to partition an interval $[0,1]$ in three equal parts by bisecting . The points that you can construct this way are $0,1$ and points of the form $\frac{n}{2^k}$.
Mar
21
comment What is the probability that the “smartest” of them has IQ score above 120?
"the smartest of them has IQ score above 120" is the opposite of "all of them have IQ score below 120"
Mar
20
comment Basic Math Question equation to equal 21
$6/(1-5/7)$ You have use parantheses. There is no way if you do not use parantheses.
Mar
8
comment How can you measure out six liters of water?
based on the idea of @Kaladin: fill the 9 liter buckte and remove 2 time 4 liter with the 4 liter bucket then 1 liter remains. put this in the tube. so you can fill the tube win an arbitrary integer number of liters
Mar
8
comment Do we need to formally teach the Greek Alphabet?
@Carl Mummert: t was talking about the 20th century. I have the impression that this alphabet is not used often today ( I would have some explanation for this). But maybe my observation is wrong.
Mar
7
comment Limit, 0/0, square roots
My advice did not work :-(
Mar
7
comment Limit, 0/0, square roots
I would try $$1-y^3=(1-y)(1+y+y^2)$$ to make the denominator rational. Take $y=\sqrt[3]{5-x}$
Mar
5
comment Approximating 'big' ratio with 'small' ratio
as other stated you should use continuous fractions. continous fraction will find $\frac{1}{3}$ and $\frac{3}{7}$
Mar
5
comment Approximating 'big' ratio with 'small' ratio
so for a given $\alpha=\frac{m}{n}$ and $v \in \mathbb{N}$ you want to find the minimal $q \in \mathbb{N}$ such that there is a $p \in \mathbb{N}$ that $$|\alpha - \frac{p}{q}| \lt 10^{-v}$$ Is this right?
Feb
27
comment $x^2-1$ with prime factors < 100
I think this is this paper: math.leidenuniv.nl/~fnajman/FLFNMC.pdf
Feb
23
comment Can subsequences be finite?
-1 $a_1, a_2, a_3, a_3, a_3, \cdots$ is not a subsequene
Feb
22
comment An equation, where the solution does not exist, but on solving the equation we got a solution. why this is happening?
process your solution procedure in reverse order: substitute your solution for x in the equation. when it first hapens that it is not a solution then figure out what happened
Feb
19
comment $\angle ABD=38°, \angle DBC=46°, \angle BCA=22°, \angle ACD=48°,$ then find $\angle BDA$
Is there a precise definition for elementary geometry? Congruent triangle , compass and ruler constructions, what else?
Feb
19
comment $f(f(x))=f(x)$ question
@fatmattxle yes
Feb
19
comment $f(f(x))=f(x)$ question
$f(x)=0,x \in \mathbb{Q}$, else $f(x)=\pi$. is a function that is not continous and has this property
Feb
19
comment $f(f(x))=f(x)$ question
Combine some of these three: $f(x)=x,x>0$, $f(x)=const, x<0$
Feb
17
comment Grandi's series contradiction
no, it is not a contradicition. closed under addition means that any finite sum of integer is an integer. Are you talking about finite sums of integers? What are you talking about? It is a contradiction of you say $S=0$ and $S=1$ because the numbers $0$ and $1$ are different in $\mathbb{Z}$
Feb
17
comment Regions in $\mathbb{C}$ containing rectangles
@5xum No, if $\Omega$ is the rectangle $1,i,-1,-1$ an the right triangle is $0.9, 0, 0.9i$ the 4th vertex is $0.9+0.9i$ which is not in $\Omega$
Feb
17
comment Regions in $\mathbb{C}$ containing rectangles
@Marcin Łoś No, if $\Omega$ is the rectangle $1,i,-1,-1$ an the right triangle is $0.9, 0, 0.9i$ the 4th vertex is $0.9+0.9i$ which is not in $\Omega$