Square Through Squares

[Strange]

3 minutes ago, mathspassion said:

dear it is very simple but do you know how this formula came into existence if not in the next quote i will define you i have already proved  through points .o.k wait for.......

Uncool explained how it relates to counting points in the previous post. He/she is obviously much smarter than me and was able to understand what you are doing in your method. 

But I’m afraid I still can’t follow your description. If you were willing to explain the steps, I might be able to. But it isn’t important, if you don’t want to. 

Does your “*” mean “max” (instead of multiply) as uncool suggested? That might be the info I was missing. 

[uncool]

Strange - it doesn't mean max. It means number of lattice points in a rectangle with the two given dimensions. This gives the formula "(Ath Sq. on X-Axis) * (Bth Sq. on Y-Axis)" = (A+1)*(B+1). For example, mathspassion, am I correct in saying that (2nd Sq. on X-Axis)*(4th Sq. on Y-Axis) = 15?

10 hours ago, mathspassion said:

dear it is very simple but do you know how this formula came into existence if not in the next quote i will define you i have already proved  through points .o.k wait for.......i have done lot work on (more then 20 years).

I don't know what you mean by "how this formula came into existence"; I have provided a geometric proof (or at least, the summary of one), which is what you asked for.

[Strange]

17 minutes ago, uncool said:

It means number of lattice points in a rectangle with the two given dimensions. This gives the formula "(Ath Sq. on X-Axis) * (Bth Sq. on Y-Axis)" = (A+1)*(B+1).

Aha! Got it. It makes sense now. 

And, (sorry for belabouring this, but it has taken me all this time to understand the original post!) this explains 4 (N - 1) + (N - 2)^2 = N^2.

Using (Ath Sq. on X-Axis) * (Bth Sq. on Y-Axis)" = (A+1)*(B+1) we can see that:

[(N-2)^th Sq. on Y-Axis] * (3^rd Sq. on X-Axis) = (N-1) * 4

[(N-3)^th Sq. on Y-Axis] * [(N-3)^th Sq. on X-Axis] = (N-2) * (N-2)

So the OP's equation for N2 = (N-1) * 4 + (N-2) * (N-2)

And we are back where we started.

[mathspassion]

16 hours ago, Strange said:

Aha! Got it. It makes sense now. 

And, (sorry for belabouring this, but it has taken me all this time to understand the original post!) this explains 4 (N - 1) + (N - 2)^2 = N^2.

Using (Ath Sq. on X-Axis) * (Bth Sq. on Y-Axis)" = (A+1)*(B+1) we can see that:

[(N-2)^th Sq. on Y-Axis] * (3^rd Sq. on X-Axis) = (N-1) * 4

[(N-3)^th Sq. on Y-Axis] * [(N-3)^th Sq. on X-Axis] = (N-2) * (N-2)

So the OP's equation for N2 = (N-1) * 4 + (N-2) * (N-2)

And we are back where we started.

thnxs a lot for sense now  but to be very frank as you related the formula with  N2 = (N-1) * 4 + (N-2) * (N-2)  that,s i do not know  but how this formula N2 = (N-1) * 4 + (N-2) * (N-2) came into existence I know I have proved two formulas for cube or square through points on pyramid .ok it,s happened all of a sudden when i was working on straight line divided into same ratio got another line again divided into same ration till i got the one point  then the miracle happened and got amazing results.

For kind information i never manipulate formulas .... for every formula i have the basic concept from wher and how this formula i got. ok.

thnxs for quoting and keep continue 

 

 

17 hours ago, uncool said:

Strange - it doesn't mean max. It means number of lattice points in a rectangle with the two given dimensions. This gives the formula "(Ath Sq. on X-Axis) * (Bth Sq. on Y-Axis)" = (A+1)*(B+1). For example, mathspassion, am I correct in saying that (2nd Sq. on X-Axis)*(4th Sq. on Y-Axis) = 15?

I don't know what you mean by "how this formula came into existence"; I have provided a geometric proof (or at least, the summary of one), which is what you asked for.

I have proved and have proof of this formula which you mentioned  and two more too. o.k dear.

[Bignose]

On 6/1/2018 at 5:21 AM, mathspassion said:

For kind information i never manipulate formulas .... for every formula i have the basic concept from wher and how this formula i got. ok.

then, mathspassion, you need to go and learn some algebra. Because the 'proof' is simply variable manipulation.

If your namesake is true, and you have a passion for maths, you should be trying to learn as much of it as you can. And algebra is a very fundamental building block of math. 

Not only that, but if you learn algebra, you'll be able to express ideas -- like the one that started this thread -- into a more succinct and generally understandable format. Strange was not the only one who struggled to understand what you were trying to say. Learning the terminology and nomenclature that you will learn in algebra will help you convey your messages much, much easier. It is worth the effort.

[mathspassion]

On 6/2/2018 at 10:17 PM, Bignose said:

then, mathspassion, you need to go and learn some algebra. Because the 'proof' is simply variable manipulation.

If your namesake is true, and you have a passion for maths, you should be trying to learn as much of it as you can. And algebra is a very fundamental building block of math. 

Not only that, but if you learn algebra, you'll be able to express ideas -- like the one that started this thread -- into a more succinct and generally understandable format. Strange was not the only one who struggled to understand what you were trying to say. Learning the terminology and nomenclature that you will learn in algebra will help you convey your messages much, much easier. It is worth the effort.

For your namesake bignose do not try to tell me know algebra my dear I know very well first you read all the quotes then write dear after reading few quotes u are not suppose to write anytning anywhere ok

Edited June 3, 2018 by mathspassion

[Bignose]

3 hours ago, mathspassion said:

For your namesake bignose do not try to tell me know algebra my dear I know very well first you read all the quotes then write dear after reading few quotes u are not suppose to write anytning anywhere ok

no. not ok. Firstly, this is a forum. Everyone who follows the rules is allowed to post.

Secondly, it is just advice. It is worth exactly what you paid for it. Feel free to take it or not. I am simply trying to help you by showing you the tools that, well, every other person who does math uses. Again, if you have ideas on a certain subject, it usually helps to learn the terminology and language of that subject. One would think that being able to better describe an idea would be a good thing.

But hey, you do you. Do whatever you want. 

 

Edited June 3, 2018 by Bignose

[Strange]

5 hours ago, mathspassion said:

For your namesake bignose do not try to tell me know algebra my dear I know very well first you read all the quotes then write dear after reading few quotes u are not suppose to write anytning anywhere ok

Why are you so totally obnoxious to someone giving you good advice?

When I was simply trying to understand your method you refused to explain and just made insulting comments instead. Luckily for me, someone else was able (and willing) to explain what you were doing.

You need to change your attitude. You can start by not using “dear” (a term of affection) when you are insulting people. 

So, my advice is: (a) grow up and (b) learn algebra. 

[mathspassion]

6 hours ago, Strange said:

Why are you so totally obnoxious to someone giving you good advice?

When I was simply trying to understand your method you refused to explain and just made insulting comments instead. Luckily for me, someone else was able (and willing) to explain what you were doing.

You need to change your attitude. You can start by not using “dear” (a term of affection) when you are insulting people. 

So, my advice is: (a) grow up and (b) learn algebra. 

hello my advice  also for you do not write grow up and learn algebra first you understand o.k and we use dear for as a respect not for affection .very well said i am insulting what you and others doing you are not aware of it   wonder full .