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I call this, "Three Squares".
All permuations from (1,1) to (1001,1001) were tested by below BASIC program and only (1,1) was found as an answer.
This is an infintesimal subset of all infinity yet untested.
for x = 1 to 1001
for y = 1 to 1001
g = x^2 + 3*y
h = y^2 + 3*x
j= g^0.5
k= h^0.5
m=int(j)
n=int(k)
if (m=j) and (n=k) then print x;" ";y
next y
next x
print x;" program ended ";yHere we can share shapes we have come up with that have ten marked locations.
The point is that one may integrate the shape into their mind's eye and utilize the shape to remember digits in base-10.
Any pictures are welcome with the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 noted on them.
You can take the same picture and number it a different order if you want to create another one similar.
This thread could be useful for basically anyone at any level of mathematical understanding.
Each picture may be accompanied by a name if you wish to provide one.
Here is what I call "Ten Piano Circle 2012".
Sorry, I don't do formal proofs until I turn 65 and so thats a couple decades off when I'm smarter.
We'll talk then somemore.
2 > 1.(9) by an infintesimal amount so close to zero, you can't see it, it has no notatable value we currently no of I guess.
But I think 2 is larger because imagine if you have lived an infinite times before now and there was no beginning. Guess what, you could have lived all those infinite lifetimes in countries that have an even number of letters in their name. Some other guy could have lived in the odd number of letters countries. So as you can see infinity, even though it can go forever and ever, it can still be confined, and one infinity can be a subset of another infinity. Such as the number line going negative forever, but then you can creep forward on the number line each lifetime counting yet more lifetimes, and still you will never get to the right side of the infinite line, in fact, you might argue, you can never even get to the zero in the middle, which means we might still be way back near infinity in the negative and don't expect ever to get very far at this rate...
Okay, get this insprination!!!
If a spring is 300 feet long and has one turn or two turns then they both have about 300 feet of metal as that
takes over. So there is the answer!!! The 3 turn spring in your problem has more metal in volumej!!!!!!
I am pretty sure. Do you see why??? It is because the length of the spring takes dominance as shown above in the 300 foot example with only 1 or two turns and a very small thickness like under a foot or an inch.
Maybe someone can do a better analysis as this is very simple.
It might be exactly the same believe it or not, but this is only sketchy calculations and
using 5 rings instead of 5 turns and 3 rings instead of 3 turns, so it is probably not exactly
the same thing. But let's say there are three springs instead of two and one has no space in the
middle because the spring thickness is double the radius. Now take three circle areas for an
approximation instead of volumes. The volume of the r=half and rmax = 1 and rmin = 0, i mean
area of the circle is just 1 times pi, ignore pi just call it one. There is no center to subtract off for this one.
Now for the donut shape of radius equal to 1 and a half or 1.5 then 2 squared (max radius) minus 1 squared (min radii),
which is 3. So the r=1.5 goes to 3pi or just 3 if we are doing proportions.
so far we have R=1, SO 0.5:1 and 1.5:3 (3 IS AREA OF DONUT LOOKING FROM TOP)
Now we do donut with r = 2.5 or 2 and a half. rmin = 2, rmax = 3
3 squared minus 2 squared = 9 - 4 = 5 and 2.5:5 is the ratio.
ratios obtained:
.5:1
1.5:3
2.5:5
Now do a fourth one r = 3.5.
4^2-3^2=16-9=7
3.5:7
So they go up by odd numbers like the squares...
So in this simplification the answer is the same for each spring.
Now we should consider the fact that the spring slants in a spiral
instead of remaining flat.
But I don't know how to do that.
In your example r=5, the perimeter center line of spring is 10pi times 3 turns = 30.
And in your example the r = 3 perimeter center line of spring is 6pi times 5 turns is 30.
both are 30.
So the answer must be pretty close I think.
Maybe someone can do a better analysis as this is very simple.
Thanks again to mf for the longer number. I appreciate it. I like to try to memorize numbers that end if 22 in the last week.
bbbndy: thanx for the interesting details you've seen and learned about digital calculations on our purchasable equipment.
Also, you see a long time ago when it quarantined my compiler or linker, it asked me should we delete it, and i said, yes, delete it thinking it had got a virus in it and was different. Now I need to find a new C compiler and linker someday that is preferably free, so I can port if needed any syntactical changes and get my 1000 to 10000 digit calculator working again.
Terrific! Thank you. What year did you write this latest "full precision calculator"? It is different than the other one from 2005 or 6, I think, and quite a marvel too!!
Yeah, it's been about sixty-one days since a lowering of my meds my 10%, the antipsychotic.
It's been quite a learning experience. Modern day drugs are unbelievable. Just a tiny 10%
change and I'm still not used all of the changes that I have seen. I guess whatever you are
ready to see, life will throw it at you!!
I feel very happy and particularly stable, and who i want to be, altogether. It's pretty nice.
How are you and how do you feel?
http://www.library.dmu.ac.uk/Images/Selfstudy/Harvard.pdf
http://www.library.dmu.ac.uk/Images/Sel … arvard.pdf
This is awesome. It tells all kinds of citations, like from
email, web sites, wiki, lectures, books, you name it, and all Harvard style.
You need to be able to read pdf's, like adobe reader, you might have, if not get adobe reader, its free.
Yeah, I've been reading lots of stuff on the net about a cube root algorithm,
and then i was reading about a smart guy who can find 13th roots in his head in a speed contest,
but his methods are not revealed, and he is not doing the decimal parts, he is only doing ones
that come out to natural numbers for the answer, but starting with 200 digit long numbers.
Amazing, but not really on the subject because he is probably doing a lot of narrowing down by
multiplying quickly in his head and readjusting until he gets the answer, but still, whatever his
method, the article didn't say.
I've heard prime numbers are good for little more than encryption, but now this might be a new one for people to work on, including myself I guess. I bet it will be a tough going project to get to the higher prime roots, could take years of trial and error. But first I'll have to see the various cube root algorithms, and then see if anyone has higher prime ones on the net.
Yeah, that's what I just kind of saw with the intermittant post #14 seconds before yours.
Yeah, I think you just need the prime number root algorithms really.
Because 65536 or 2**16 or 2^16 when square rooted 4 times on the calculator goes down to 2,
via 256, 16, 4, 2, so that kind of points to 2*2*2*2=16, so
hence
cube root follwoed by another cube root would be 3x3=9th root.
Hmmm.... cube roots, that's an interesting thought. Now fifth roots would be next since 4th roots are just square roots twice, so then after that I guess 7th roots would be next to learn since the cube root and square root sequence is probably the sixth root, is that right, or is it 2x3 or 2+3?
Oh, yeah, I've heard of the Samarians or some people with a similar name that did the 60 thing.
Did you know the 12 on the clock may have come from Egyptians counting knuckles on one hand?
Hmmm, base-60, wow, I think I could put the numbers in parethesis instead of using 26 upper/lower case = 52 + 8 numbers.
I think I could just do (45) (46)... (59), (01)(00),(01)(01), for the writing system.
But as for the times table, it could be printed out with a simple little BASIC program I guess, but do you recommend base-60 first, over base-4 for some reason. Will it be more fun or something?
Sweet, thanks for the encouraging word on the algorithm holding over bases. I will experiment sometime in the next month when I feel the urge to learn it more. I think I will make a times table in base-4 and an adding table in base-4 to help me out in the hand calculations.
Hey that's awesome. That brings back a lot of memories of reading that when I was little.
Nice example. So the 20 is actually a doubling and then you add one more digit (chiffre).
Thnks for da link, though it had http-http twice in a row so it failed, but anyway, it's not
your fault, there is a glitch in the system it seems, so i reposted. But this is really awesome.
I think I will finally remember it for a long time, especially if I use it a few times on paper
tomorrow.
The link is funny so I fixed it:
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
Woops, I mean 54/100, not 53/100. I must have a glitch in my typing or something because I swear I typed 54, weird.
My silly calculator again does not know which one is the right one
for the square root of 422. Can someone give me more digits
on this too, thanks!