golden ratio new formula

Here is a quick list of outputs for (-x+sqrt((x*x+4)))/2

Quick random analysis:

for x= -9.9 (-9.9 + sqrt(-9.9*-9.9+4))= 10

so 9.9 squared is 98.01, so the square root ( 98.01 + 4 ) + 9.9 must be exactly 20 then divide by 2 to get the 10

9.9 + 10.10 = 20

cheers, Jamie

x f(x)

-10 10.09901951359

-9.9 10.00000000000

-9.8 9.90099990002

-9.7 9.80201978994

-9.6 9.70306026885

-9.5 9.60412195974

-9.4 9.50520551069

-9.3 9.40631159618

-9.2 9.30744091838

-9.1 9.20859420856

-9 9.10977222865

-8.9 9.01097577279

-8.8 8.91220566907

-8.7 8.81346278129

-8.6 8.71474801093

-8.5 8.61606229914

-8.4 8.51740662898

-8.3 8.41878202770

-8.2 8.32018956920

-8.1 8.22163037672

-8 8.12310562562

-7.9 8.02461654638

-7.8 7.92616442784

-7.7 7.82775062064

-7.6 7.72937654088

-7.5 7.63104367407

-7.4 7.53275357935

-7.3 7.43450789403

-7.2 7.33630833845

-7.1 7.23815672118

-7 7.14005494464

-6.9 7.04200501113

-6.8 6.94400902933

-6.7 6.84606922128

-6.6 6.74818792991

-6.5 6.65036762718

-6.4 6.55261092285

-6.3 6.45492057393

-6.2 6.35729949498

-6.1 6.25975076914

-6 6.16227766017

-5.9 6.06488362543

-5.8 5.96757233004

-5.7 5.87034766211

-5.6 5.77321374946

-5.5 5.67617497768

-5.4 5.57923600978

-5.3 5.48240180765

-5.2 5.38567765544

-5.1 5.28906918496

-5 5.19258240357

-4.9 5.09622372448

-4.8 5.00000000000

-4.7 4.90391855782

-4.6 4.80798724080

-4.5 4.71221445045

-4.4 4.61660919472

-4.3 4.52118114028

-4.2 4.42594066992

-4.1 4.33089894559

-4 4.23606797750

-3.9 4.14146070008

-3.8 4.04709105536

-3.7 3.95297408448

-3.6 3.85912602820

-3.5 3.76556443707

-3.4 3.67230829233

-3.3 3.57937813816

-3.2 3.48679622641

-3.1 3.39458667457

-3 3.30277563773

-2.9 3.21139149538

-2.8 3.12046505341

-2.7 3.03002976164

-2.6 2.94012194669

-2.5 2.85078105936

-2.4 2.76204993518

-2.3 2.67397506541

-2.2 2.58660687473

-2.1 2.50000000000

-2 2.41421356237

-1.9 2.32931142241

-1.8 2.24536240471

-1.7 2.16244047484

-1.6 2.08062484749

-1.5 2.00000000000

-1.4 1.92065556157

-1.3 1.84268604419

-1.2 1.76619037897

-1.1 1.69127122105

-1 1.61803398875

-0.9 1.54658560997

-0.8 1.47703296143

-0.7 1.40948100502

-0.6 1.34403065089

-0.5 1.28077640640

-0.4 1.21980390272

-0.3 1.16118742081

-0.2 1.10498756211

-0.1 1.05124921973

0 1.00000000000 0.1 0.95124921973 0.2 0.90498756211 0.3 0.86118742081 0.4 0.81980390272 0.5 0.78077640640 0.6 0.74403065089 0.7 0.70948100502 0.8 0.67703296143 0.9 0.64658560997 1 0.61803398875 1.1 0.59127122105 1.2 0.56619037897 1.3 0.54268604419 1.4 0.52065556157 1.5 0.50000000000 1.6 0.48062484749 1.7 0.46244047484 1.8 0.44536240471 1.9 0.42931142241 2 0.41421356237 2.1 0.40000000000 2.2 0.38660687473 2.3 0.37397506541 2.4 0.36204993518 2.5 0.35078105936 2.6 0.34012194669 2.7 0.33002976164 2.8 0.32046505341 2.9 0.31139149538 3 0.30277563773 3.1 0.29458667457 3.2 0.28679622641 3.3 0.27937813816 3.4 0.27230829233 3.5 0.26556443707 3.6 0.25912602820 3.7 0.25297408448 3.8 0.24709105536 3.9 0.24146070008 4 0.23606797750 4.1 0.23089894559 4.2 0.22594066992 4.3 0.22118114028 4.4 0.21660919472 4.5 0.21221445045 4.6 0.20798724080 4.7 0.20391855782 4.8 0.20000000000 4.9 0.19622372448 5 0.19258240357

Some things are too important to leave at home.

ChesterW

I found this page showing the same formula I made:

They even call the golden ratio numbers silver and bronze, I just called them all golden :)

Nice shirt :D

cheers, Jamie