A universal relationship!!!

As I was playing with my calculator trying to find a direct relationship between the two mathmatical constants π (Pi) and φ (Phi) -- something remarkable happened. I actually made it!!! Obviously, this is not the right forum for mathematics, but since there are no subforum here dedicated to math, and since I'm always looking for a lady who would find stuff like this fascinating, here we go:

A few years ago, while fiddling with my pair of compasses and the usual straightedge, I discovered a way to design a perfect ten-pointed star. Being quite sturdy in geometry, but not so good at arithmetics, I didn't seem to be able to actually prove it in a formula or equation. Constructing the star, what I did was I divided the radius of a circle in the golden proportion and used this measure to plot a decagon (or a ten-sided polygon/star). But how would I explain this with numbers and letters? That there was a direct relationship between Pi and Phi in a way I had never seen elsewhere? Seeing π*φ equals roughly 5, I realised that the extra decimals would simply be there due to the fact that the circumference of a circle is slightly longer than the perimeter of a decagon or a pentagon. And the perimeter of a polygon is given by:

==> 2nr sin(π/n) where n is the number of sides and r is the radius

Given my circle and decagon shared the diameter equaled to 1 (thus the circle has a circumference of π, since 2πr=c), I came up with the following:

==> 5 / (2*10*0.5 sin(π/10)) = φ = 1.618033989...

or in other words ==> 5 divided by the perimeter of a decagon with diameter 10 equals the golden number Phi precisely. Now. Does anyone else find stuff like this eh, what's the word-- sexy?

I think I deserve at least a lesser goddess for this discovery....

a reply to: Utnapisjtim

Sorry, but you can count me out of this equation baby !!

Yep, unless lightning strikes me, and the sum result of this lil' ordeal is a mathematical genius new brain, which is highly unlikely btw, then defo count me out.

Oh but on the plus side I am a Goddess at working out 70% reductions on fashion items !!
On the minus side, I do it waaaaay too often

a reply to: uk today

Dang! A Goddess and all....

Speaking of the devil, I guess King Solomon was right when he said:

"If a man offered for love all the wealth of his house, he would be utterly despised."

So... What if I only offered my love, but with a 70% discount? Would that still offend thee?


ETA: A friend of mine once hypothesised that the sum of attraction in a relationship was constant, let's say 1, where a perfect relationship would be around 50/50 attraction-wise. The more desperate or heart-struck person #1 would be, the less interested person #2 would then be and so on. However, according to my friend, a 50/50 relationship would seldom form, since it would simply be too mundane and well, sensible. And love is anything but sense. 70/30 however. It might've actually worked

originally posted by: Utnapisjtim

==> 5 / (2*10*0.5 sin(π/10)) = φ = 1.618033989...

or in other words ==> 5 divided by the perimeter of a decagon with diameter 10 equals the golden number Phi precisely.

That should be diameter 1, not 10 of course.

originally posted by: Utnapisjtim

originally posted by: Utnapisjtim

==> 5 / (2*10*0.5 sin(π/10)) = φ = 1.618033989...

or in other words ==> 5 divided by the perimeter of a decagon with diameter 10 equals the golden number Phi precisely.

That should be diameter 1, not 10 of course.

And simplifying or reducing the fraction, gives an even sexier equation:

==> 2 sin(π/10) = φ = 1.618033989...

There you go, phi defined with pi using trigonometry.

The "normal" way to define phi is:

==> (√5+1)/2 = φ = 1.618033989...

Someone linked me to this.
I literally made an account just so I could reply to this.
I think math is sexy.
Oh so *very* VERY sexy.
Especially the Golden Ratio.
Know how the pentagram (five-pointed star) is infinitely Golden-Ratioed?
Makes sense that the decagram could be in some sense, too

a reply to: Utnapisjtim

I have a universal relationship with my palm, usually the left.... sometimes the right.....

I know exactly how you feel.

originally posted by: PteroFractal
Someone linked me to this.
I literally made an account just so I could reply to this.

Hehe, looks like I have a fan

I think math is sexy.
Oh so *very* VERY sexy.
Especially the Golden Ratio.

I recommend a book called "A beginner's guide to constructing the universe". Tons of golden ratio stuff. It features the numbers between 1 and 10 with an incredible amount of info gathered for each number.

Know how the pentagram (five-pointed star) is infinitely Golden-Ratioed?
Makes sense that the decagram could be in some sense, too

Yes, a decagon is basically two pentagons/pentagrams on top of eachother, one pointing up and another pointing down. I use a slightly different way to construct the decagon, but the way wikipedia does it is quite elegant:

==> en.wikipedia.org...

a reply to: Hijinx

There is a trick in the Bible concerning this:

"When you give to the needy, do not let your left hand know what your right hand is doing" Matthew 6:3

Apparently, Jesus was a mamzer so I guess he had quite a bit of experience with the kind of love you deal with....

a reply to: Utnapisjtim

A 70% discount on love is pretty cool, but I feel I'm getting a lil' ripped off here !!

Duh....just because moi cannot solve the numbers puzzly thingy, which is VERY scary looking indeed, does not mean that moi is not aware that love is FREE

a reply to: uk today

One love, one free golden love!

To be honest, I don't really understand that above either. It just works! I'm afraid it's the case of a phenomena described in the infinite monkey theorem:

I took a calculator and punched in those buttons on it, and the result was the golden number: φ or Phi. And what the hell, there was π in there too, another one of those Greek letters and it turned out to be quite simple and elegant after a bit of shavings. For all I know it's some kind of calculator magic known only for certain post apocalyptic priests in the future who are constantly scavenging the Earth for triple-A batteries to keep their God alive, the Casio fx-9860GII

Would be great if someone who actually knew trigonometry could explain exactly what the hell the equation does, for that looks like an awful simple way to define Phi on a calculator. So I figured I'm a bleeding genius, like I reinvented gunpowder or something. Had I found some hidden shortcut and some magic way to define Phi with Pi?

Anyone? Why does 2 sin(π/10) equal Phi? I can't seem to figure it out.

a reply to: Utnapisjtim

Holy #e that construction GIF is sexy as # *_*
I uh... *adds to my... "pretty pictures" folder*
Yeah. Pretty pictures folder. xD

I'll look into that book, hehe :3
Would essentially be like porn to me, but hey. I like this material for other reasons, too. xD

And yep. In a sense. I don't understand this site. Dunno how to use it at all.
But someone on another site linked me to this post.
You called for a girl that thought math is sexy.
Someone told me someone was searching for such.
I answered. xD I had to! How can I not?

Seriously, it's so #ing goddamn sexy.
Graham's number... yum. Big numbers.
Golden spiral... delicous.
Don't get me started on fractals

a reply to: PteroFractal

Oh dear. Such charming words....

a reply to: Utnapisjtim

Now really. How the hell do I use this site? I can't even find the User Control Panel o.o

a reply to: PteroFractal

I suggest reading through the terms for starters. As for settings and such: The round downward-arrow in the main menu reveals a submenu. Try that.

a reply to: Hijinx

A friend is always nice.

originally posted by: PteroFractal
a reply to: Utnapisjtim

Holy #e that construction GIF is sexy as # *_*
I uh... *adds to my... "pretty pictures" folder*
Yeah. Pretty pictures folder. xD

I'll look into that book, hehe :3
Would essentially be like porn to me, but hey. I like this material for other reasons, too. xD

And yep. In a sense. I don't understand this site. Dunno how to use it at all.
But someone on another site linked me to this post.
You called for a girl that thought math is sexy.
Someone told me someone was searching for such.
I answered. xD I had to! How can I not?

Seriously, it's so #ing goddamn sexy.
Graham's number... yum. Big numbers.
Golden spiral... delicous.
Don't get me started on fractals

What a friggin' idiot I am! When you replied to this I had happened to've fallen in love with a person who later turned out to be an absolute frogs' arse who played with me feelings like I was Tetris or something. If you ever drop by again, I would love to hear from you! I DO love intelligence, and I would love to get to know you better.

I have to come with a confession, since religion is also one of my favorite subjects. I once cybered with a lady who was big as a mountain, but her mind was so beautiful that I honestly loved her and still admire her, but I can't seem to find her anywhere. Not only was she beautiful for her mind alone, but also the incredibly fascinating ability to make love with candles and turn them into perfect circles. She actually had a huge collection of them in a box stuck under her bed. It was in the morning of May 17th which happens to be my country's Constitution Day (Norway). Such intelligence as her's and hopefully yours is so rare to find. And yeah, I know, I probably shouldn't have said that, neither to you or on this site at all. Please say you will drop by again and say «Hi, wanna date?» or something. I am willing to give ye a second chance.