A formula for Pythagoreans with prime roots

[Dr.Peterson]

The problem was explained at the beginning of the text, which is: "How to use a right-angled triangle to find a point on the number line"
The problem is that if we use a triangle, we have to draw an arc from the highest vertex of the triangle, which we have to open from a caliper with an opening the size of the hypothesis. This is because I say that the sides must have numerical relationships with each other because If the sides have no numerical relationship with anything and we put this, we will not reach the answer that the "problem" wants.

But that problem is perfectly well solved; as far as I can tell, you think it isn't because you are either doing the wrong construction, or the wrong calculation. You are making claims about factors and primes that have nothing to do with this construction. And your formula seems unrelated to it. The appropriate "numerical relationship" is just the Pythagorean theorem, which you seem to be misunderstanding.

Here, for example, is a construction of [imath]\sqrt{3}[/imath]:

Constructing the square root of 3

mathcentral.uregina.ca

(If what you want is [imath]1+\sqrt{3}[/imath], start the construction at 1.)

Here is a construction of the square root of any small whole number:

https://www.ck12.org/flexi/math-grade-8/irrational-numbers/how-do-you-draw-the-square-root-of-3-on-a-number-line/

These all work. Your formula does not.

 

[Vast3]

But that problem is perfectly well solved; as far as I can tell, you think it isn't because you are either doing the wrong construction, or the wrong calculation. You are making claims about factors and primes that have nothing to do with this construction. And your formula seems unrelated to it. The appropriate "numerical relationship" is just the Pythagorean theorem, which you seem to be misunderstanding.

Here, for example, is a construction of [imath]\sqrt{3}[/imath]:

Constructing the square root of 3

mathcentral.uregina.ca

(If what you want is [imath]1+\sqrt{3}[/imath], start the construction at 1.)

Here is a construction of the square root of any small whole number:

https://www.ck12.org/flexi/math-grade-8/irrational-numbers/how-do-you-draw-the-square-root-of-3-on-a-number-line/

These all work. Your formula does not.

These are all obtained from a geometric solution, but if we want to use only algebra, we will run into problems.

 

[Dr.Peterson]

These are all obtained from a geometric solution, but if we want to use only algebra, we will run into problems.

Please SHOW US those problems that you think exist, in comprehensible terms. They do not exist.

The Pythagorean theorem is geometry; it involves a calculation that does work. If it did not, then it would not be a theorem.