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.
-
LIVE
Chad Prather
50 minutes agoJimmy Kimmel Is FIRED After Horrific Charlie Kirk Comments + Trump Designates ANTIFA As Terrorists!
435 watching -
55:01
The White House
2 hours agoPress Conference with the Prime Minister of the United Kingdom of Great Britain and Northern Ireland
1.25K4 -
Barry Cunningham
59 minutes agoBREAKING NEWS: PRESIDENT TRUMP PARTICIPATES IN PRESS CONFERENCE IN ENGLAND
2 -
LIVE
Badlands Media
8 hours agoBadlands Daily: September 18, 2025
3,790 watching -
LIVE
JuicyJohns
2 hours ago $0.61 earned🟢#1 REBIRTH PLAYER 10.2+ KD🟢
52 watching -
DVR
Matt Kohrs
11 hours agoStocks Squeeze To New Highs 🚀🚀🚀 || Live Trading (OPEN, NVDA & TSLA)
11.8K2 -
45:23
Randi Hipper
1 hour agoBITCOIN PRICE MOMENTUM PICKS UP! CRITICAL LEVELS TO WATCH
4.72K1 -
11:33
Mrgunsngear
13 hours ago $4.03 earnedBreaking: This NFA Exempt Firearm Is Now Available With No Stamp - This Is HUGE 🇺🇸
8.3K21 -
1:09:24
The Mike Schwartz Show
3 hours agoTHE MIKE SCHWARTZ SHOW with DR. MICHAEL J SCHWARTZ 09-18-2025
5.37K5 -
LIVE
Wendy Bell Radio
6 hours agoGood Night, Jimmy
7,239 watching