ASCIi Group

Site Seekers

Each month, a member of the group will give a brief presentation on web sites. Some members present sites based on the same theme (for example, real estate), others tell us about sites that cover a broad range of subjects.

2006

March - Hank Pearson
- Google Suggestions
  http://www.google.com/
  - Google finds defintions and offers spelling suggestions. When you use the 'define:' operator but misspell the word or phrase, Google (now) asks if you mean something else. For example:
    
    define: red hairing
    
    Did you mean:
    define: red herring
  - When you click the suggestion, you see some definitions:
    
    define: red herring
    
    Definitions of red herring on the Web
  - But sometimes you find other defiitions by leaving out the colon:
    
    define red herring
    
    One such link (you would not have found using the colon) is to Answers.com:
- Answers.com
  - red herring:
    Definition and Much More from Answers.com
    http://www.answers.com/topic/red-herring...
    
    The red herring article in Answers.com includes information from Wikipedia about the Red Herring magazine, headquartered in Belmont, California. When you click the Belmont, California link, ...
  - Belmont, California
    http://www.answers.com/topic/belmont-cal...
    
    ... you see all kinds of interesting information about the city: geography, weather, demographics, ...
    
    On that page, when you search for Phoenix, ...
  - Phoenix
    http://www.answers.com/Phoenix?cat=trave...
    
    ... note that Phoenix is the sixth largest city in the US, and the 13th largest Metropolitan Statistical Area (MSA).
- Largest Cities
  - Cities by Population
    http://www.answers.com/main/ntquery?meth...
    
    Pictures of the 40 largest cities
  - Metropolitan Areas
    http://www.answers.com/main/ntquery?meth...
    
    The top 25 metropolitan areas
  - Principal Agglomerations of the World
    http://citypopulation.de/World.html
    
    468 cities of a million or more
- Exploring Answers.com Categories
  http://www.answers.com/
  
  Across the top of the home page, there are categories, like Business, Entertainment, Health, People, Places, Reference, Science, Shopping, and Words. Click Science, for example, and then Math. Look at all the math articles. Click F to see articles that start with F - several pages. Click Next, Next, Next, Fibonacci Number.
- Fibonacci Numbers
  http://www.answers.com/topic/fibonacci-n...
  
  "A series of whole numbers in which each number is the sum of the two preceding ones: 1, 1, 2, 3, 5, 8, 13, etc."
  - Fibonacci Numbers and Nature
    http://www.mcs.surrey.ac.uk/Personal/R.K...
  - Fivefold and Spiral Symmetry
    Associated with Fibonacci Sequence
    http://www.geocities.com/CapeCanaveral/L...
  - The human face
    is based entirely on Phi
    http://goldennumber.net/face.htm
  - Beauty is in the phi of the beholder
    http://goldennumber.net/beauty.htm
  - Fibonacci Calculations
    #calculations
  - Fibonacci Macro
    #macro
  - Fibonacci Drawsing
    #drawing

Fibonacci Calculations

Columns:

n	sequential number (current iteration)
fib	Fibonacci number (sum of previous two Fibonacci numbers)
sq	square of current Fibonacci number
cum	accumulation of squares
prod	current Fibonacci number times next Fibonacci number
~Phi	next Fibonacci number divided by current Fibonacci number
~phi	previous Fibonacci number divided by current Fibonacci number

n	fib	sq	cum	prod	~Phi	~phi

1	1	1	1	1	1.0	0.0
2	1	1	2	2	2.0	1.0
3	2	4	6	6	1.5	0.5
4	3	9	15	15	1.666667	0.666667
5	5	25	40	40	1.6	0.6
6	8	64	104	104	1.625	0.625
7	13	169	273	273	1.615385	0.615385
8	21	441	714	714	1.619048	1.619048
9	34	1156	1870	1870	1.617647	0.617647
10	55	3025	4895	4895	1.618182	0.618182
11	89	7921	12,816	12,816	1.617978	0.617978
12	144	20,736	33,552	33,552	1.618056	0.618056
13	233	54,289	87,841	87,841	1.618026	0.618026

Note:
cum = prod
Phi = phi + 1

The fractional parts of Phi and phi (right of the decimal point) are equal.

Phi and phi are the aspect ratios of rectangles formed by drawing squares of Fibonacci numbers.

To perform these calculations, I wrote the following Microsoft Word macro (which you can copy and paste):

Fibonacci Macro

Sub Fibonacci() ' calculations demo

Dim fib(14)
fib(0) = 0
fib(1) = 1
cum = 0

Selection.TypeText Text:= _
"Fibonacci Calculations" & vbCrLf & vbCrLf & _
"Columns:" & vbCrLf _
& vbCrLf & "n" & vbTab & _
"sequential number (current iteration)" _
& vbCrLf & "fib" & vbTab & _
"Fibonacci number (sum of previous two Fibonacci numbers)" _
& vbCrLf & "sq" & vbTab & _
"square of current Fibonacci number" _
& vbCrLf & "cum" & vbTab & _
"accumulation of squares" _
& vbCrLf & "prod" & vbTab & _
"current Fibonacci number times next Fibonacci number" _
& vbCrLf & "~Phi" & vbTab & _
"next Fibonacci number divided by current Fibonacci number" _
& vbCrLf & "~phi" & vbTab & _
"previous Fibonacci number divided by current Fibonacci number" _
& vbCrLf & vbCrLf & _
"n" & vbTab & _
"fib" & vbTab & _
"sq" & vbTab & _
"cum" & vbTab & _
"prod" & vbTab & _
"~Phi" & vbTab & _
"~phi" & vbCrLf & vbCrLf

For cur = 1 To 13 ' current iteration n
nxt = cur + 1 ' next
prv = cur - 1 ' previous

fib(nxt) = fib(prv) + fib(cur)
sq = fib(cur) ^ 2

cum = cum + sq
prod = fib(cur) * fib(nxt)

cap_phi = fib(nxt) / fib(cur)
phi = fib(prv) / fib(cur)

Selection.TypeText Text:= _
cur & vbTab & _
fib(n) & vbTab & _
sq & vbTab & _
cum & vbTab & _
prod & vbTab & _
Round(cap_phi, 6) & vbTab & _
Round(phi, 6) & vbCrLf
Next

End Sub ' Fibonacci

Fibonacci Drawing

Suppose you lived about 2500 years ago and started drawing adjacent squares to form rectangles as I have drawn below. Each square has a side as large as the previous rectangle. After drawing several squares, you draw an arc in each square from corner to corner:

Fibonacci Squares and Arcs

Note the sizes of the squares (the Fibonacci numbers) and the ratios of the sides of the rectangles (that tend to Phi, the golden number).