Thread: What is this called and why is it true or is it true?

I tired searching this on the internet and could not find an answer.


Why is it that when you take any number and square it and then take the numbers one higher than that number and one lower than that number and then multiple them, they will always be one less than the number you get when you square it?

Example One :

1 x 1 = 1

0 x 2 = 0

Example Two :

-5 x -5 = 25

-4 x -6 = 24


Just so you know I am horrible at math and have not tested this with too many numbers and do not really know if it works with all numbers or just many numbers or just the ones I tested. Also I tend to flip the mess out of everything in my head. I also do not know if this is already widely known or anything and if it is I would like to know the name of it.

It's simple algebra.


See here if you don't know how to multiply binomials as above.
http://www.themathpage.com/alg/quadratic-trinomial.htm

Ok thank you, probably learned it sometime in school and forgot about it. Also do we know why numbers and math work?

Another way to think of it is by using "counters". Take a 5x5 set of counters.
* * * * *
* * * * *
* * * * *
* * * * *
* * * * *
Then imagine taking the top right one away, giving 5^2 - 1
* * * *
* * * * *
* * * * *
* * * * *
* * * * *
Then you can take the top row of only four, and move it over to the far right as a sixth column. This produces a 4 x 6 array.
* * * * * *
* * * * * *
* * * * * *
* * * * * *
I suppose this really only "proves" it for whole numbers, but it should be satisfying for most people who don't need rock solid proof for everything.
Everything we know about numbers and math has been derived using logic and reasoning, like the logic above.

Thank you both for being nice and trying to explain how things work, but I think I learned I should try to not learn these things or anything dealing with science or math or programming or reading or any other intellectual field at least for the time being.

I just read a little bit of your post, but I do not want to take the time to try to understand it. Maybe going on this forum was the wake up call I needed.

A good way to find what you are good at is first finding the things you are not good at.

I have been praying to God to help me understand my place or basically just a job or somewhere I can be productive and happy and not make anyone else feel bad and to do good in this world.

I started remedial math at the 5th grade level about a year and a half ago, and I'm doing Precalculus now. It just takes practice and patience, Deepblah. As for what you should be doing in the world, try starting by finding a relationship between what you enjoy doing and a possible career.
This may require that you believe in YOURSELF. Just a thought.

Originally Posted by deepblah123

Ok thank you, probably learned it sometime in school and forgot about it. Also do we know why numbers and math work?

I don't think anyone knows the answer. It's a question of philosophy. Some think the universe is inherently mathematical. Others think the universe is inherently random but it's our minds that are inherently mathematical.