# Starting with e and Pi…how do you get to Phi? [closed]

No equations...need one line answer only.

No tricks here.. $$e$$, $$\pi$$, $$\phi$$ are regularly used universal constants.

Here is the one line answer:

Starting with $$e$$ and $$\pi$$ as Fibonacci seeds, do hundred iterations and take the ratio of last two terms to get to $$\phi$$.

If you want, you can do more to improve accuracy to multiple decimal places.

## closed as off-topic by Omega Krypton, El-Guest, Glorfindel, Brandon_J, Jeff ZeitlinMay 31 at 12:29

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• No equations please..just one sentence answer..can be elegantly explained in about 15 words or less.. – Uvc May 31 at 11:06
• I am really puzzled by downvotes..puzzle is explicitly stated..very concise..no equations needed..simple understanding of mathematical process is all you need to give the answer!! – Uvc May 31 at 11:38
• Is this right and can it be expressed in words? $\phi = e^{i \pi / 5} + e^{-i \pi / 5}$ – Weather Vane May 31 at 12:54
• Yeah: that's not exact. The ratio of terms from a Fibonacci series oscillates around $phi$ with alternate terms above and below, only being $phi$ at the infinite term. – Weather Vane May 31 at 14:33
• So, the intended answer is equivalent to "Starting with $e$ and $\pi$, chuck both in the dumpster. Do Fibonacci to get the answer." How very elegant. – Bass May 31 at 23:20

The product of e square and pi cube is approximately equal to six hundred divided by phi cube.

In formula

$$\pi \approx \bigg(\frac{600}{(e\phi)^2}\bigg)^{1/3}$$
EDIT: $$e^2\pi^3 \approx \frac{600}{\phi^2}$$

Found @

• Not the one I am looking for..you start with e and pi..end up with phi – Uvc May 31 at 11:22
• @UVC Is it fine now? – Ak19 May 31 at 11:28
• No..you start with e and Pi and end up with Phi..that process can be stated in one sentence – Uvc May 31 at 11:30
• This is accurate only to 3 decimal places. – Gareth McCaughan May 31 at 11:35
• @Gareth..if we are thinking on the same lines, it should be lot more accurate after 20 steps or so...let me do some quick calculations and will get back to you – Uvc May 31 at 14:23