[(r/4+r)/H*r*(r/4+r)]^2+[(r/4+r)/H*r*(r/4+r)]^2= sqrt{Pi*r^2}...Expressed inside a Euclidean plane (r/4+r)^2+(r/4+r)^2= sqrt{3.125*r^2}...Non Euclidean These two calculation are exactly equal in the real world and solve the "Quadrature of a circle" problem If you use anyone of these techniques depending on what universe you choose to measure inside you will get the same physical structure for any perfect circle of infinite different radiuses
"See how I related H above to a specific geometric relationship between a circle, a square, and a second square as a justification to introducing H into that specific discussion. Well here, I have no discussion, just a bare, naked, trivial fact that you did not know." You have my attention here please explain this "H = Γ(½) × (½)^(½)" in detail because I have also noticed this in my own way just cant explain clearly this is a key point to understanding what going on in my visualisations. "By claiming to "know" your "fundamental argument is sound" you are in fact claiming to have the prerequisites to know that. This appears untrue. Logic and mathematics are not some final steps in communication requiring some "translation" -- they are the first steps in thinking that are required to have your viewpoint be shareable." I still stand by my claims... "I'm not the one who wastes other people's time after coming to them for instruction, so kindly leave your comments about the ugliness of my personality at the door." I was talking about myself I actually think you have a great personality you are very honest and lack sarcasm you actually make factual arguments based on facts or lack of facts which I can always respect regardless of what side of the argument I sit on, you think before you speak and comprehend before you reply this approach I respect
rpenner is paying you the rope, and you just keep wrapping it around your neck. No, it's not unfamiliar to us. It's covered in school. It's just not part of the system of weights and measures the British used here in the colonial era. But the US academies standardize around the International System (SI) which simplifies calculations in that all the units are normalized. And that excludes the Celsius scale, leaving you, and all nationals steeped in Celsius, with the task of converting to Kelvins. But then all of those citizens who studied science are fluent in SI, so really we are all on the same page. Leaving the misfits as those folks who never bothered to do well in science. And they would rely on Farenheit and/or Celsius depending on custom.
The Euclidean version is not necessary for the construction both circles will be completely identical the only circles that is not identical or not circles but polygons or simply imperfect circles
actually no, incorrect. i use SI and/or metric all day long . i never use american units or what ever they are called. when i was in college, one of the first lessons are teaching SI and unit conversions. they taught us, TF =1.8(Tc)+32 TC = TF-32/1.8 TK = TC +273
Draw a line of any distance "r" divide by four equal lengths using Euclid's methods of equilateral triangles then construct a square using a compass (r/4+r)^2 measure the hypotenuse distance of this square so...... (sqrt{(r/4+r)^2+(r/4+r)^2})^2=3.125*r^2 this can only be calculated with ease if you use the pi ratio "3.125" but will physically be the same when constructed as long as its a perfect circle, so all perfect circles of different diameters or the same.
Correct as always, but I had in mind the simple observation that -40F = -40C and for every block of 5C degrees above that common value there are same number of 9degree blocks above that -40 on the F scale. Krash661 in post 28 gives the two more standard but memorized only formulae - not much understanding in them. With understanding you can get quick nearly correct transform either way "in your head." In the same "nearly correct / in you head" spirit I always liked pi = 22/7. only about 0.04% too high & who would not like a slightly bigger slice of pie?
I am trying to communicate my concept of how I solved the "Quadrature of a circle" the equations are made out of the process I carried out in reality and verified myself so I wanted some second opinions.
"(r/4+r)^2+(r/4+r)^2=3.125*r^2...non Euclidean" "[(H*r/r/4+r) r/4+r]^2+[(H*r/r/4+r) r/4+r]^2= Pi*r^2....Euclidean" corrections made
That claim does not follow from the axioms of any particular discussed example of non-Euclidean geometry. In fact, it happens to be a simple algebraic claim which holds true regardless of choice of geometry. The notion that \(\frac{25}{8}\) may be substituted in for π in algebra or geometry was examined and found to be baseless and untrue. http://www.sciforums.com/threads/this-thread-is-for-rpenner.143300/#post-3251925 By returning to a claim that was proven untrue, you are doing the opposite of learning and being the opposite of fair. That claim does not follow from the axioms of geometry, algebra or arithmetic. Indeed, the claim reduces following standard rules of algebra to \( \frac{\pi}{2} = \left( \frac{H}{16} + \frac{r}{4} + 1 \right)^2\) With solutions \( H \in \left\{ 16 \sqrt{\frac{\pi}{2}} - 4 r - 16, \quad - 16 \sqrt{\frac{\pi}{2}} - 4 r - 16 \right}\), that is the expression is neither constant with respect to r, a single-valued function of r, or universally positive for positive values of r. If \(r \geq 2 \sqrt{2 pi} - 4\) then \(H \leq 0\), which is nonsensical in Euclidean geometry.
I am not forming a final conclusion yet am just presenting the evidence, and the steps allowed me to solve to quadrature problem. basically my formula is saying a^2+b^2=c^2... then c^2= pi*r^2 I put up instructions on how to construct it why don't you construct it yourself and take the measurements, you should get c=sqrt{pi*r^2} that satisfies the parameters of the task. The challenge was to construct a square with the same area as a circle using only a straight edge and a compass I believe I have demonstrated this "c^2= pi*r^2"...
Ok, sorry I think you must be doing something I do not know, what is the quadrature of circle, I thought you meant 1/4 section of the circles circumference, but after looking it up, do you mean the total area of a 1/4 section of a circle? And can you put a index to your maths example c=circumference a=area r=radius h=?
Quadrature is a historical mathematical term that means determining the area. 2000 years ago the only legitimate technique was to construct with straightedge and compass a square with the same area as the given figure. Since squaring the circle is impossible, this was doomed. But since the area of similar figures is proportional to the square of a length associated with the figure and all circles in Euclidean geometry are similar then it follows that the area of the circle is proportional to the radius squared, r². From reasoning by analogy with other symmetrical plane figures, the area of the circle was known to be ½ r × circumference and since circumference = 2 π r, the area of the circle is known to be πr². But π, was not a rational number and not the root of any polynomial equation with rational coefficients thus it requires a concrete grasp of real analysis to get a handle on it. But approximations like 22/7 and 355/113 have long been known to be good approximations.
My thesis statement " The ratio of a circles circumference to its diameter is it rational or irrational? countless examples has demonstrated that it is irrational, proofs such as lambert Tan(pi/4)=1, the seemingly impossible construction of the quadrature of a circle, and proof that supports its transcendental nature pi is not the root of any polynomial with rational coefficients."
