# π/Φ Pi in the Phi

#### sly1

##### Heartless
Registered Senior Member
Forgive me if I am lacking in the mathematics department but I have some questions...

I was messing around with numbers (as I like to do) and noticed what I thought was something interesting relationship wise between (Piπ)3.141592 and (PhiΦ) also known as the golden ratio 1.618033

Two relations...

(Φ*2) = 3.236066 pretty close to the number (π) 3.141592
The difference between (Φ*2) 3.236066 and (π) 3.141592 is roughly 0.094474

(π/2) = 1.570796 pretty close to the number (Φ) 1.618033
The difference between (Φ) 1.618033 and (π/2) 1.570796 is roughly 0.047237

What I find interesting is that 0.047237*2 is exactly 0.094474

The difference between the ~Pi and the real Pi is exactly 2x more than the difference between the ~Phi and the real Phi...

also

(Φ+Φ = 3.236066) - (π/2 = 1.570796) = 1.66527

1.66527 - Φ = 0.047237

Thanks ahead of time for any help/explanation

You're just computing Phi minus half pi a number of different ways. For example of course your second number is half the first, you just divided everything by 2. Then your last expression is Phi + phi - pi/2 - phi = phi - pi/2. Same thing, no surprise.

pi phi issue are better than pie-fighting issues of other threads. I'm just saying.

You're just computing Phi minus half pi a number of different ways. For example of course your second number is half the first, you just divided everything by 2. Then your last expression is Phi + phi - pi/2 - phi = phi - pi/2. Same thing, no surprise.

What I guess intrigues me is that there seems to be some underlying relationship between the two separate "ratios"..

As much as I was aware they were two separate ratios calculated separately and therefor independent of one another.

I find it odd I guess that difference between Phi*2 and the real Pi is exactly 2 times Pi/2 and the real Pi...

I don't know if I'm correctly explaining this lol

What I guess intrigues me is that there seems to be some underlying relationship between the two separate "ratios"..

$$\pi$$ is not a "ratio". $$\pi$$ is transcendental. The golden ratio is not transcendental.

$$\pi$$ is not a "ratio". $$\pi$$ is transcendental. The golden ratio is not transcendental.

yea this is true pi is not a ratio...however they are still two completely different "numbers" that are derived through two completely different means but apparently are showing something similar and that is

0.047237 and 0.047237*2

the only thing I'm doing in the above is comparing the doubling of Phi and the halving of Pi and the differences between those numbers to to each other.

I will refrain from referring to pi as a ratio, sorry about that miss communication.

yea this is true pi is not a ratio...however they are still two completely different "numbers" that are derived through two completely different means but apparently are showing something similar and that is

0.047237 and 0.047237*2

the only thing I'm doing in the above is comparing the doubling of Phi and the halving of Pi and the differences between those numbers to to each other.

I will refrain from referring to pi as a ratio, sorry about that miss communication.

AlphaNumeric explained why you are getting the results you are getting.

AlphaNumeric explained why you are getting the results you are getting.

yes I understand HOW i got the results but I don't understand WHY it is they are so similar when they are based off of two completely different numbers one being based off of Phi and one be based off Pi...

I wouldn't expect similarities between the two numbers regardless of any operational pattern I used...they are different so If I halve one and double the other they shouldn't be able to be reduced to a common number...

I understand HOW I got the numbers I got...i didn't accidentally do this...I am confused on WHY they are showing any similarity at all.

I just figured out why/what...and I feel like a dumbass lol....having said all that thanks to those who tried to enlighten me I appreciate it!

~sly~

$$\pi$$ is not a "ratio". $$\pi$$ is transcendental. The golden ratio is not transcendental.

Last time I checked, $$\pi$$ was the ratio of a circle's circumference to its diameter.

Last time I checked, $$\pi$$ was the ratio of a circle's circumference to its diameter.

Of course, it seems Tach got a little too cocky in his answer. You are right James.

SMBC comics (by Zach Weiner)

Bonus...

Last time I checked, $$\pi$$ was the ratio of a circle's circumference to its diameter.

Tsk, tsk. Pete's rebuttal is funnier. You need to stop stalking, it makes you look bad. Especially unworthy for a moderator.

Tsk, tsk. Pete's rebuttal is funnier. You need to stop stalking, it makes you look bad. Especially unworthy for a moderator.

Let's see:

Tach said:
$$\pi$$ is not a "ratio". $$\pi$$ is transcendental. The golden ratio is not transcendental.

Clearly, contrary to your claim, pi is a ratio, as I explained to you.

It is not a ratio of two integers, but then I never claimed that it was. You, on the other hand, made the bald statement that "pi is not a ratio" of any sort.

So, while I'm sure you'll go on for a few more pages trying to worm your way out of your latest error, you still stand corrected. Again.

very interesting convo I feel like something will come out of this...hmm

now I know what you speak of op do some research on the kepler triangle it's "coined" as a "mathematical coincidence" or so they say lol but anyways they say its almost equal to because if it was equal to then pi would be rational.

Look. Here's what happened way back in 2011:

Two relations...

(Φ*2) = 3.236066 pretty close to the number (π) 3.141592
The difference between (Φ*2) 3.236066 and (π) 3.141592 is roughly 0.094474

In mathematical terms: $$2\Phi- \pi = 0.094474$$

The difference between (Φ) 1.618033 and (π/2) 1.570796 is roughly 0.047237

That is: $$\Phi - \pi/2 = 0.047237$$

What I find interesting is that 0.047237*2 is exactly 0.094474

But $$2(\Phi - \pi/2) = 2\Phi - \pi$$

so there's nothing particularly interesting about that.

That's that then.
See you all again in 3 years time.

I personally also, am not great at the maths and like yourself, like to experiment playing with the numbers. You will find the more experimental procedure you do using a differential of the present used values, you will make coincident's from the numeric values.
You will also find that adjusting the value of Pi, by decimal placing and values, you will make more relationships such has m/s to mph conversion.
The misconception you are missing, that I missed also, it that the relationship of numbers and multipliers etc, will always allow a person to give the same values or close, by playing with numbers.
This is because in history the basics of the maths were based on the rotation of the Earth, and the values they use now , ''work'', for the Physical actions.
In changing the values, we would have to change the Physics of the process.

This is because in history the basics of the maths were based on the rotation of the Earth, and the values they use now , ''work'', for the Physical actions.

If a rod has a diameter of 1 unit it has a radius of .5 units. The rod has a circumference. The circumference is measured in the same units. If you measure the circumference with a length of (theoretical) string, the length of the string is always 3.1416 (rounded off) times 1 unit of diameter. So 29.072 units of diameter means the circumference of the rod is 29.072*3.1416 units. Pi*D=Circumference.

If in reality you measure the string length and it was 3.64 times the length of 1 unit of diameter then pi would be 3.64, but that's not the case in reality. In reality if you measure the diameter and then measure the circumference, it's always circumference/diameter=3.1416 (rounded off).