Please help amateur mathematician

[Phil Jurd]

Instead of counting sheep before going to sleep, I attempt maths problems. I have calculated three equations which I feel certain have already been documented, perhaps thousands of years ago. I remain curious though, of by whom and when they were first written. I have not plagiarized any of the three, nor have I put pen to paper in arriving at the following three equations, all done in my head with the lights out.

1. (X + 1) cubed minus X cubed = (2X + 1) squared minus X times (X + 1)......Let us assume that X = 9 therefore .....
1,000 minus 729 = 19 squared or 361 minus 10 x 9 or 90 or
271 = 271

2. The sum of the internal angles of any shape, where the sides are equal = the number of sides minus two sides times 180 degrees
Therefore a twelve sided shape has the sum of the internal angles equal to 12 -2 = 10 times 180 or 1,800 degrees.

3. (X + 1 ) squared minus X squared = 2X + 1

Many thanks for any and all help satisfying my curiosity

Phil

 

[stapel]

Instead of counting sheep before going to sleep, I attempt maths problems. I have calculated three equations which I feel certain have already been documented, perhaps thousands of years ago. I remain curious though, of by whom and when they were first written. I have not plagiarized any of the three, nor have I put pen to paper in arriving at the following three equations, all done in my head with the lights out.

1. (X + 1) cubed minus X cubed = (2X + 1) squared minus X times (X + 1)......Let us assume that X = 9 therefore .....
1,000 minus 729 = 19 squared or 361 minus 10 x 9 or 90 or
271 = 271

2. The sum of the internal angles of any shape, where the sides are equal = the number of sides minus two sides times 180 degrees
Therefore a twelve sided shape has the sum of the internal angles equal to 12 -2 = 10 times 180 or 1,800 degrees.

3. (X + 1 ) squared minus X squared = 2X + 1

Many thanks for any and all help satisfying my curiosity

What is your question? Are you asking if these are "famous" equations? Or if they're valid? Or something else?

Please be specific. Thank you!

 

[fcabanski]

Read some math books. You can't think about math, especially new math concepts, without knowing what's already known and understood. In other words stop reinventing the wheel.

 

[HallsofIvy]

Help how? And how satisfy your curiosity? You didn't ask any questions. What you have are pretty much standard 8th or 9th grade algebra-geometry problems.

 

[Ishuda]

Instead of counting sheep before going to sleep, I attempt maths problems...

Hi Phil

The interior angles result goes back to Euclid I suspect and certainly to Euclid or earlier for the triangle. The other two I haven't seen specifically although they can be shown to be true fairly easily, especially if you use pen and paper.

As an aside, I also do 'math problems' in going to sleep. One is to find the fastest growing series. Now actually there is no fastest growing series but I run through definitions in my head working up to an intermediate series for which the first few terms are
S(1) = 1
S(2) = 4
S(3) = 7625597484987
and S(4) is so large that if each atom in the know universe represented a digit, there still would not be enough digits to write the number.

 

[HallsofIvy]

Help how? And how satisfy your curiosity? You didn't ask any questions. What you have are pretty much standard 8th or 9th grade algebra-geometry problems.

If you are going to quote me, at least put quote marks around. And give some reason for quoting.