Premium Only Content

Expanded Patterns of Phi
Welcome to my video on an expanded pattern of Phi, or the Golden Ratio. I'm going to be showing how this pattern is manifested in a series of parabolas.
Part I shows the basics of this expanded Phi pattern in the parabolas and their respective quadratic equations;
In Part II, I add right triangles to the parabolas, and show how the ratios of their sides are connected in an unexpected way;
Part III shows how the Golden ratio and the Silver ratio are both essential parts of the parabola described by x^2-x-1;
And in Part IV we look at how the Fibonacci series enters into all this. The means of using the Fibonacci numbers to get this expanded Phi pattern is similar to, but not the same as, the way it's used to get the Silver and other Metal ratios.
-
1:09:09
Omar Elattar
8 hours agoThe Brain Experts: Your Brain Can Rewire Itself At Any Age & Here's How!
18K3 -
LIVE
IcyFPS
4 hours agoLIVE - Wuchang Fallen Feathers x Borderlands w/ pope!
504 watching -
29:24
Afshin Rattansi's Going Underground
18 hours agoWas Epstein a Mossad Agent? Will Obama go to Prison? (Afshin Rattansi vs Alan Dershowitz)
26.5K22 -
4:26:54
Nerdrotic
11 hours ago $30.38 earnedFantastic Four Baby Steps V Superman's James Gunn, South Park Returns | Friday Night Tights 364
110K8 -
3:17:40
megimu32
4 hours agoOFF THE SUBJECT: FAFO Friday! Cops, Crash, Kombat & Chaos!
24K5 -
10:17:28
GrimmHollywood
13 hours ago🔴LIVE • GRIMM HOLLYWOOD • CLIP FARMING 101 •
19.9K1 -
1:07:56
Glenn Greenwald
11 hours agoIsrael-Made Famine Crisis Finally Recognized | SYSTEM UPDATE #493
106K66 -
2:29:42
TheSaltyCracker
6 hours agoGhislaine Maxwell Talks ReEEeStream 7-25-25
95.5K196 -
9:27
MattMorseTV
9 hours ago $3.45 earnedHe just lost EVERYTHING.
27.4K11 -
5:52:21
a12cat34dog
7 hours agoSPOOKY ASS 2005 GAME :: F.E.A.R. :: FIRST-TIME FINISHING THIS CLASSIC {18+}
9.35K10