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I think it is extremely perplexing here quod it is filled with members who smell like feet, but somehow they actually manage to smell differently as I have struggled to climb up lorries, which resemble large...
Hannah,
Mathematics is fun when you try to understand the subject.
Trying to memorize the tables and the formulae may be difficult for some.
Yet, it is easier to get a good score in Mathematics than any other subject.
For example, When you forget what 7x7 is,
try to remember what 7x6 is, then add 7 to the result.
You can get doubts clarified here.
mathsyperson wrote:MathsIsFun wrote:Proofs are just way too strict.
Where did I say that?
Anyway, I agree with me.
Mathematical proof is based axioms and proven theorems, and proofs are viewed throough a microscope.
Euler had claimed x^4+y^4+z^4=w^4 had no solutions;
In 1988, Naom Elkies of Harvard University discovered that
2,682,440^4 + 15,365,639^4 + 18,796,760^4 = 20,615,673^4
Merely testing the first million numbers cannot constitute a mathematical proof!
Maybe, I should have waited for some more days
before giving the solution.
Your reply seems convincing!
I shall take hard copies of your posts,
study them all again, then again,
before finally saying,
"You are right, Mathsy!"
Give me just a few days!
What is a limerick, Mother?
It's a form of verse, said brother
In which lines one and two
Rhyme with five when it's through
And three and four rhyme with each other.
There once was a boy named Reece
He ate and ate until he was obese
He had a big belly
and stuffed it with jelly
and all he wanted for his tummy was peace.
There once was a young boy named Nick
Who by chance was always being kicked
He tried not to fight
For he was smart, kind and bright
So he learned how to run really quick.
There once was an artist named Saint,
Who swallowed some samples of paint.
All shades of the spectrum
Flowed out of his rectum
With a colourful lack of restraint.
There once was a fly on the wall
I wonder why didn't it fall
Because its feet stuck
Or was it just luck
Or does gravity miss things so small?
Speed = Distance travelled / Time taken
Let the distance travelled in 1 circle be C Units.
Speed of A = C Units/hour and Speed of B=6C Units/hour.
I'm not good at proofs, but this is my attempt:
c is a constant, so there is only one value for y.
As shown in the expansion of y109376, the important coefficient will always take the form 2(y*6), because 6 is always the last digit. This means that this proof can be carried forward for any point on the chain of the magic number.[/proof]
There's probably a flaw in there somewhere, could someone check it please?
I am unable to find any serious flaw, yet,
I am not fully convinced.
I shall try with a much simpler number, viz. y76.
y76 is (y*10^2)+(7*10^1)+(6*10^0).
When this number is squared,
[This is of the form (a+b+c)²
which is equal to a² + b² + c² + 2ab + 2bc + 2ac]
we get
10000y² + 4900 + 36 + 14000y + 840 + 1200y
which is the same as
10000y² + 15200y + 5776
From this, it is clear, for any y belonging to Natural Numbers,
the last two digits are not affected. They continue to be 76.
But, does this conclusively prove there exists a value y such that
the last three digits of y76² are y76?
Mathsy, I am confused.
... oh no, will he ever catch A?
Reminds me of Zeno's Paradoxes!
B is faster than A and would get past him eventually!
We are only interested in the 10^6 coefficient of the square of this. That will be equal to 2(y*(6*10^0))+a constant made up of the expansion of the other powers of 10, but that does not involve y.
So, the 10^6 coefficient is 12y+c, which should only be equal to y for one value of y.
We are only interested in the last digit of 12y+c, so it can be called 2y+c without affecting our purposes. However big c is, it can also have all of its digits except the last removed.
Mathsy, how did you get '2(y*(6*10^0))+a constant made up of the expansion of the other powers of 10, but that does not involve y'?
Consider giving a link to the calculator on the Index page,
since not many may be aware, when the link is in this forum.
Two cyclists A and B go in circles,
A takes 1 hour to complete one circle,
and B completes 6 circles (the same circle as A) in an hour.
The question is, if the two start, in the same direction at
07.30 AM, when would they next cross each other?:)
Yes, good thing he did. Now the problem is open to all, other than you, Mathsy.
Both x! and x^y work, but for larger values, as you rightly pointed out, it becomes very slow.
However, a useful tool.
This has got nothing to do with the proof,
I was just a bit inquisitive!:D
42576576769103890995893380022607743740081787109376
Mathsy, did you get this number too by exhaustion, just like you got the 30 digits????:)
I have put the numbers from 1 to 10 in three groups. Tell me, on what basis have I grouped the numbers. I shall give you a clue, but I am not sure if that would be of any help
CLUE
(1,2,6,10) RED
(4,5,9) BLUE
(3,7,8) GREEN
I'll give my opinion tomorrow on Mathsy's proof, when I start the day afresh;
Regarding including n!, it would be of immense help as combinatorics works mostly on
factorials;
nPr= n!/(n-r)!
and
nCr = n!/(n-r)!*r!
nPr gives the number of Permutations
and
nCr gives the number of combinations.
There is an approximation for factorials of higher numbers;
it is called the James-Stirling formula
n! is approximately equal to
√(2*Pi*n) multiplied by (n/e)^n
This is a brilliant approximation as the value of n goes up.
You are right, Mathsy!
I think I should have put this in Puzzles and Games.
The layout is fine. Would it be possible to add 2^n? Thats the most important of powers.
And also n! if possible.
And Mathsy, its difficult to prove or disprove that there would always be a number in the sequence. But I strongly feel, the sequence would go on and on.
Thanks, Rora,
but I don't understand how,
when I change the signature,
it changes in the earlier posts too!
A cylinder 6 inches in diameter is partially filled with water. A sphere 3 inches in diameter is gently dropped into the cylinder. To what further height does the water rise in the cylinder?
This can be explained in another way.
when you have a/b=c/d,
you get ad=bc.
In this problem,
3/(5x+1) = 2/9,
therefore, 9x3 = 2(5x+1)
27=10x+2
Move 2 to the other side, by changing the sign,
27-2 = 10x,
25=10x,
x = 25/10 = 2.5
Wow! Great job by you two!
I got to really thank both of you, Admin for putting the calculator on the site,
and Mathsy for making my job pretty easy!
I had 17 digits with me already, now you have given me 30!
I know, Mathsy, you have done a lot of homework....
Testing for all numbers 0-9 for twenty digits is a demanding job....
it requires squaring to be done 200 times! ( after 1787109376)
Regarding my ideas, my explanation is (not too sure),
2 and 5 are numbers that perfectly compliment each other in multiplication,
and I go back to my earlier post....
The last n digits of powers of 2 start repeating at every
2^(4 x 5^n-1). This is a hypothesis, it isn't proven yet.
It works till 2^2500, beyond that, not too sure! 2^2500 ends in 09376.
This is indeed, a great work by the Mathsisfun team!
The beguiling ideas about science quoted here were gleaned from essays, exams, and classroom discussions. Most were from 5th and 6th graders. They illustrate Mark Twain's contention that the 'most interesting information comes from children, for they tell all they know and then stop.
Q: What is one horsepower?
A: One horsepower is the amount of energy it takes to drag a horse 500 feet in one second.
You can listen to thunder after lightning and tell how close you came to getting hit. If you don't hear it, you got hit, so never mind.
Talc is found on rocks and on babies.
The law of gravity says no fair jumping up without coming back down.
When they broke open molecules, they found they were only stuffed with atoms. But when they broke open atoms, they found them stuffed with explosions.
When people run around and around in circles we say they are crazy. When planets do it we say they are orbiting.
Rainbows are just to look at, not to really understand.
While the earth seems to be knowingly keeping its distance from the sun, it is really only centrificating.
Someday we may discover how to make magnets that can point in any direction.
South America has cold summers and hot winters, but somehow they still manage.
Most books now say our sun is a star. But it still knows how to change back into a sun in the daytime.
Water freezes at 32 degrees and boils at 212 degrees. There are 180 degrees between freezing and boiling because there are 180 degrees between north and south.
A vibration is a motion that cannot make up its mind which way it wants to go.
There are 26 vitamins in all, but some of the letters are yet to be discovered. Finding them all means living forever.
There is a tremendous weight pushing down on the center of the Earth because of so much population stomping around up there these days.
Lime is a green-tasting rock.
Many dead animals in the past changed to fossils while others preferred to be oil.
Vacuums are nothings. We only mention them to let them know we know they're there.
Some oxygen molecules help fires burn while others help make water, so sometimes it's brother against brother.
Some people can tell what time it is by looking at the sun. But I have never been able to make out the numbers.
We say the cause of perfume disappearing is evaporation. Evaporation gets blamed for a lot of things people forget to put the top on.
To most people solutions mean finding the answers. But to chemists solutions are things that are still all mixed up.
In looking at a drop of water under a microscope, we find there are twice as many H's as O's.
Clouds are high flying fogs.
I am not sure how clouds get formed. But the clouds know how to do it, and that is the important thing.
Clouds just keep circling the earth around and around. And around. There is not much else to do.
Water vapor gets together in a cloud. When it is big enough to be called a drop, it does.
Humidity is the experience of looking for air and finding water.
We keep track of the humidity in the air so we won't drown when we breathe.
Rain is often known as soft water, oppositely known as hail.
Rain is saved up in cloud banks.
In some rocks you can find the fossil footprints of fishes.
A blizzard is when it snows sideways.
A hurricane is a breeze of a bigly size.
Thunder is a rich source of loudness.
Isotherms and isobars are even more important than their names sound.
It is so hot in some places that the people there have to live in other places.
The wind is like the air, only pushier.