You are not logged in.
Think of how many books are incorrect about digital computers making “real random numbers” now. How long before this is corrected in schools and colleges?
woodturner550
I am afraid that many books are also incorrect about many other things (while many other books are correct).
We like it or not, this was always the case, for one reason or another. And it will be so till the end of time.
Therefore, the best thing that one can do is to present, as possible, what he has as 'new knowledge' without expecting any positive reaction... with the hope that his 'new knowledge' doesn't oppose, in any way, the interests of some powerful rich groups which are based on 'old knowledge'.
Interesting exercise.
Kerim
I guess you both know now that, to let this exercise have a solution, the sum 95 could be multiplied by 10 for example (and the missing 0 was simply a mistyping).
For instance, let us recall that the solution of a problem could be the null set, that is it doesn't have one.
When I was at school (then universities) and I couldn't find a solution of a problem, I went on proving that no one else can find it too
by proving it cannot exist in the first place (as you did).
With x=0.12 why does m, the gradient, =infinity? I thought it would equal zero as there is zero slope?
Good question. Here are two ways, I think of, to answer it:
[1]
x=0.12 could also be written as 0*y = 1*x - 0.12
And let us assume that the value '0' here is actually very close to 0 [not exactly 0], like 1/1,000,000,000,000 for example.
We get:
y*1/1,000,000,000,000 = 1*x - 0.12
or
y = 1*x*1,000,000,000,000 - 0.12*1,000,000,000,000
As we see, we have now m=1,000,000,000,000 and c=-120,000,000,000
In other words, we can simplify this process by saying that m=infinity and c=-infinity [while the ratio of their infinities is m/c=-1/0.12]
[2]
As you know, 'm' is the slope of the line, which is defined by the linear equation. Therefore, m = dy/dx.
Since the line is vertical on the x-axis (x=0.12 for any value of y), dx is zero for any value of dy.
m = dy/dx = dy/0 = infinity [as you know, a number divided by zero is equivalent to a very big number, infinity]
Also, 'c' is where the line intercepts the y-axis. Since both, the y-axis and the equation's line, are on the same plane and vertical on the same straight (x-axis), they are parallel. Therefore, they intersect at infinity. Again,'c' here is equal to infinity ![]()
Kerim
x=0.12
and,
y=6Those would produce points on the graph, as opposed to lines, yeah? If so, why are they classed as linear equations, if they're just points?
For instance,
x=0.12 produces a vertical line if drawn on the conventional y_x plane. [but this is a special case, |m|=infinity and |c|=infinity]
y=6 also produces a horizontal line on y_x plane. [here, m=0 and c=6]
Well, this is what I discovered too but I thought it was just me.
In brief, Wikipedia is for 'old knowledge' only. And its rules are made so that it can, when necessary, be biased legitimately about 'any topic', very clever.
You did well. It is always good to see something from different angles.
For instance, since I have no more a person to tell me if my solution of a problem is wrong or right, I used to find out different ways (two in the least) to solve it.
I guess we all know that 20x+25y=1000 is equivalent to:
y = -20x/25 + 1000/25
y = -4x/5 + 40 [m=-4/5 and c=40]
But this equation is of a special case. Its 'y' and 'x' have to be positive integers or zero only. That is not all points of the straight line which this linear equation represents are valid as a solution.
Any idea?
Did you try Wikipedia?
But am still learning.
Even at age 75, I am still learning. I am also making many mistakes before I solve the problems I am interested in.
I simply don't give up whenever I face a well-defined math problem (usually related to my designs).
On the other hand, having no interest in doing something has no remedy at all, even in the case of the most intelligent humans.
But I am afraid that the crucial starting point is self-trust. In other words, the unlimited power of the human's brain is limited by its owner only and to how far he believes it can help him. Unlimited/Limited trust results unlimited/limited intelligence (this is the practical meaning of the greatest advice said 2000 years ago).
Kerim
For instance, in year 1980, I presented a novel simple demodulator (claimed non-existent at the universities, even in these days) to the local authorities so that they can have real secure communications (being non-existent to the engineers in the developed countries).
I got many negative reactions. The worst one was in a meeting at a room in the military headquarters. I was with three persons: a (so-called) professor in electronics, his assistant and a high officer (as a supervisor). This professor insisted on saying one thing while avoiding talking about anything else: "You cannot know something not known in the West". When I knew he is a professor in electronics, I thought he was able to discuss with me, scientifically, many things about the presented project. Instead, he kept repeating that I am a dreamer while refusing to do any further step to verify if my work is real or not. After about 20 minutes, I recalled what happened to Galileo because I had the impression that I will end up be in prison if I don't play the ignorant and please that professor. So, thanks to Galileo, I was able to return home sane and safe ![]()
By the way, at the National Research Center (at the capital), I was told clearly that a local engineer has no right to work on any novel project.
Also, a high security officer was sincere with me (in private) that having secure RF communications whose sets are not imported from abroad is out of question (in other words, their so-called secure communications have to be monitored by certain foreigners).
As I mentioned earlier, I simply took advantage of my unknown demodulator when I needed to have secure private RF links for many years in the 80's.
Conclusion:
'New knowledge' has to wait till the World's Masters know (usually by their close servants) how to let it serve well their own interests and be under their full direct control too. This took about 2 centuries in case of Galileo ![]()
Kerim
Thanks again Bob. According to my workings, i got 88m. This is my workings: outside=8m, inside=6m =(8m+6m)(8m-6m) = 22/7×14m×2m=44×2=88m
Although you used the diameters instead of radiuses, I noticed you used the identity:
a^2 - b^2 = (a+b)*(a-b)
This is a clever step that usually helps to simplify the calculation.
I think you will be very good in math.
Kerim
Welcome Liu,
I guess you heard already that every big project starts always with a first small step. I hope you will be able to find out soon what your first small step could be.
From my own experience, when someone really needs to achieve something, he always ends up doing it even after zillions of failures.
Kerim
From my rather long experience, I ended up realizing that 'new knowledge' could be welcomed (assuming it is understood by some people) if it makes direct money only (or the like).
Anyway, speaking practically, 'new knowledge' in any field has to be useful to the one who needed it in the first place. For example, about forty years ago, I needed to connect my house and workplace (3 km distance) via RF voice inks. For about 5 years, I achieved this connection/communication by using a novel technique so that my RF links (on MW band then on FM band) couldn't be noticed by the radio listeners or authorities. Even in these days, this technique is supposed non-existent, at all universities around the world.
Very interesting. So far, so I might be wrong, I see just one application which can benefit from this study.
I am 75. I was fortunate that, since I was teen, I have enjoyed the most every time I had difficult math problems to be solved (numerical and logical). For example, while the boys and girls played together around the swimming pool, I enjoyed solving new math problems instead ![]()
Naturally, this helped me be an independent professional designer in electronics (hardware and software), right after finishing my high studies. Since then, I design and produce various electronic controllers which are needed by the local consumers in every period of time.
This is how I was able to gain my daily bread (and of my few assistants) while working independently.
(Please note that working independently may not be possible for engineers living in some other countries).
Kerim
As I understand it, to truncate means to chop off all the numbers after a certain decimal place, but without rounding.
I agree with you.
I usually hear "find the integer' instead of 'truncate'.
I mean, the English math's verb 'truncate' is somehow new to me. Thanks to you, I know now its meaning.
This is how I understand truncation:
6.20 to 6.2499999 gives 6.2
6.25 to 6.2999999 gives 6.3
Therefore, my answer is:
6.2 ≤ x < 6.25
For instance, the answer [ 6.2 ≤ x < 6.3 ] refers to int(x).
Kerim
While I respect all other’s interesting answers, here is mine:
The probability for Jesus to return back to the planet earth is zero.
Speaking logically (since we are in a math forum), there is no reason, at all, for Jesus to return back.
But this 'logical view' doesn’t prevent zillions of world’s men who like to see in Him an 'earthly' ultimate King (by the way, this earthly view is very clear on the Gospel during His Crucifixion), to believe that He will come back to rule, with them, the tiny planet Earth (and to live, therefore, the death of Earth as well!).
Is it hard to get what I say? ![]()
Let us recall that, on the Gospel, even the well-educated ruler, Nicodemus, who was very serious and came to Jesus to learn from Him, couldn’t understand His 'spiritual' message. Why? Well, I am afraid I have to leave it as an exercise for some of you to solve ![]()
For instance, in my life (I am 75 now), the known saying "Necessity is the mother of invention/innovation" seemed to work always.
Also, a problem will not be solved by the most intelligent human, if he doesn't have the slight interest in it.
Thanks mathxyz. I would do that. I still get confused by completing the square method. But am good with the factorization method.
For instance, I personally can't explain how it may be difficult for my brain, sometimes, to understand/solve a new idea/problem (speaking practically), then it gets it very well just by itself after a certain time (after a month, a year or too many years in some cases).
The key point is that I had to be interested to get it very seriously, for one reason or another.
Back to math, 'infinity' and 'an imaginary number' cannot be seen (or measured) outside one's mind. But their use, in solving certain problems, is very important, for one reason or another.
(Sorry, one may think that an atheist who insists to see something to believe its importance in his life cannot also believe in the importance and existence of many math's elements
)
No one told me yet what the word sin (or sinning) means in one's life exactly, speaking practically.
For instance, I would become crazy if I had to live in this material world forever. But, fortunately, the Will/Power behind my existence gave me a mortal living flesh so that my journey in it is just temporary.
After all, my best moment, after I live a long hard-working day, is the time to sleep. And the death of my living flesh is simply my last eternal sleep (but this is not the end of the story).
We like or not, by design, a living body should be alarmed (having pain) every time there is something wrong or damaged in it. Otherwise, it can't survive for long (a human baby would never have the chance to grow up and be even a kid).
Hatred, wars, corruption and whatever is called evil are typical in the material world, also by design. They are the fruit of executing the natural pre-programmed instructions embedded in every living body (natural instincts). 'Men of the world' (created to serve the material world as all other living things are) have no choice but to be guided by their natural instincts, as robots run exactly as they were programmed to do.
This is why I personally (being no more of this world) have no reason to resist or even blame the 'men of the world' because they are just robots, driven solely by their natural programs (instincts). They cannot (they are not supposed, by design) to oppose the natural instructions embedded in their living cells. In fact, about 2000 years ago, someone revealed this natural crucial truth very clearly when He forgave all His killers because "they know not what they do".
Who has ears will hear.
Perhaps they were deleted by mistake.