Durango Bill's Home Page

Origin & Formation of the Grand Canyon
Evolution of the Colorado River (Geology)
3-D Grand Canyon Geologic Tour
Ancestral Rivers of the World
Probability Analysis of Popular Games
Graph Theory Enumeration
Global Warming / Climate Change

Computer generated picture of southwest Colorado
(3-D image of Durango, CO generated by Google Earth.)

   Durango, Colorado is located in the Animas River Valley just a few miles southeast of the 13,000-ft. high La Plata Mountains. Local attractions include the Durango & Silverton Narrow Gauge Railroad, Purgatory Resort (skiing), Mesa Verde National Park, and some of the world’s most frightening highways and jeep “roads”.

e.g. Black Bear Road / Black Bear Pass:  http://en.wikipedia.org/wiki/Black_Bear_Road
“You don’t have to be crazy to drive this road - but it helps”.
For some grizzly info, run a Google search using: “saw a car that seemed to fall out of the sky”. Also check “Black Bear Pass” videos at YouTube.

About the author and his home (near the center of the picture and to the right of the small lake) where:
Sometimes it Snows in the Mountains  

 Links to Topics

Paleogeography / Historical Geology
     Evolution of the Colorado River
A model of the geologic history of the Colorado River and its tributaries starting with the Late Cretaceous through the present. Includes origin and formation of the Grand Canyon.

3-D aerial tour of the Grand Canyon
     3-D end-to-end geologic tour of the Grand Canyon
An end-to-end aerial geologic tour of the Grand Canyon. Sequencing through the pages simulates a nearly 300-mile trip starting with Glen Canyon Dam at Page, AZ., and continues past the Grand Wash Cliffs to Lake Mead.

Recommended Grand Canyon Videos
     Norman Beerger's The Grand Canyon
In 1982 Norman Beerger filmed and produced what is probably the best video ever made for anyone that would like an armchair scenic aerial tour of the Grand Canyon. Both the 1-hour and 2-hour versions are helicopter tours accompanied by a classical music sound track. The included notes can be used as a mile-by-mile guide for either the 1-hour or 2-hour versions.

Colorado Geology
     Rio Chama Rockfall - A pictorial study
A large rockfall occurred in a remote area of the upper Rio Chama headwaters sometime between Sept. 1998 and June 2005.  There appears to be no available information about the rockfall, and the author happened to find it while browsing with Google Earth.

Ancestral Rivers of the World
An illustrated world tour with examples of river systems that cut through mountain ranges instead of taking easier routes around them. The geologic processes involved are “antecedence” and “superimposition”.

Amethyst geodes and cathedrals are fascinating members of the quartz family.

Creationism, “Intelligent Design Evangelism”, Religious Cultists
     Creationism = Willful Ignorance
A brief review of the fallacies of Creationism and “Intelligent Design Evangelism”. Noah’s Flood is physically impossible, but that doesn’t stop Creationists from perverting reality in an attempt to force their religious beliefs on everyone else. Is the willful ignorance of the Creationists a result of fear?
    Patriot Bible “University”
Very few people have had a chance to see the current location of Kent Hovind’s alma mater - mostly because it’s a long way from any other “educational institution”.
     George Bush Misrepresents Science and Knowledge
Is George W. Bush one of the ignorant Young Earth Creationists?
What might happen if you combined Ignorance and Power?
If the Ignorant Armies gained control, what steps might these Creationists take to throw us back into the Dark Ages of Religious Theocracy?
Some highlights from a paper endorsed by a large number of Nobel Laureates.
    New Orleans Underwater
The funds that were supposed to be spent reinforcing New Orleans’ levee system were instead diverted to the Iraq war and the figurehead Department of Homeland Security. Thus New Orleans did not have the protection it could have had when hurricane Katrina hit.
    What causes a Creationist to be a Creationist?
The answer is:   Fear!
1) Fear of evolution.
2) Fear and hatred toward gays/lesbians.
3) Fear of women.
4) Fear of death.
5) Fear of losing their “All Powerful Father”.
    Militant Protests by Religious Cultists against “Planned Parenthood” in Durango, Colorado
A small militant group of abortion protesters has been active at Planned Parenthood in Durango, Colorado. The group is run by “Michaela Dasteel, director of LifeGuard”, and as reported in the March 16, 2007 Durango Herald, their activities include:

Game Analysis

     Bingo Probability and Statistics
The statistics, probabilities, and odds involved with the popular game of Bingo. Includes algorithms for the computations.
     Bridge Combinatorics and Probabilities
The statistics, combinatorics, and probabilities for the various point counts, suit distributions, and suit splits for Bridge hands. Includes “How To” mathematics.
   Round Robin and Whist Tournament analysis and schedules
     The Integer Brick Problem
Also know as the Euler Brick problem. No solutions out to odd side <= 1.0 Trillion (1.0E12).
     Monopoly Probabilities and Statistics
End-of-turn and "Land on" statistics/frequency analysis for Parker Brothers Monopoly Game. All the "What is the chance of landing on ..." statistics. Also, there are up to 50,083 ways to "Go To Jail".
     N-Queens Problem
How many queens (and/or superqueens) can be placed on an arbitrarily sized chessboard without any of them attacking another queen? Queens to N = 26, Superqueens to N = 23.
     Peg Solitaire (Both pages include number of solutions)
15 Hole Peg Solitaire
     This version is for a triangular pattern with 5 holes (peg positions) per side.
33 Hole Peg Solitaire
     Sold commercially as Hi-Q
     577,116,156,815,309,849,672 possible Hi-Q games
    40,861,647,040,079,968 different ways to win Hi-Q 
     Pig (Pig-out)
Optimal strategy for two versions of this dice game
     Poker Probabilities
Probabilities for 5 to 10 card hands (including misc. wild cards), lowball Poker, and optimal strategy for Video Poker.
     Shut the Box - Optimal Strategy
Includes a prototype for a casino version.
     Solitaire Chinese Checkers
The minimum number of moves to move a set of ten marbles from one side to the other is 27.

Graph Theory / Number Theory
(Valid for 47 states but not in Kansas, Louisiana, or Texas where all math/science “theories” are being thrown out as “not Biblical”.)
Epitrochoids and Hypotrochoids are curves generated by rolling one circle around another stationary circle. Examples and graphical illustrations are given.   
How many ways are there to subdivide a set containing "N" items?
     Rooted (oriented) trees
A rooted tree has a single vertex (node) desiginated as a "root" (usually at the top). Travel along any of the edges is directed toward the "root". A table is given showing how many structurally different, rooted trees exist given "N" vertices.
     Non rooted (free) trees
A non-rooted tree has a free form where no vertex has priority. A non-rooted tree can be twisted, deformed, contorted, etc. into many shapes without altering its structure. Again, a table is given showing how many structurally different, non rooted trees exist given "N" vertices.
     Ordered Binary trees
A binary tree is rooted tree where each vertex can have a maximum of two edges that connect to lower portions of the tree. The "root" is normally depicted at the top. Edges from any vertex in the tree will descend either to the left (left branch) or to the right (right branch).
     Structurally different binary trees
How many structurally different binary trees exist given "N" vertices?
     Structurally different graphs
An unlabeled graph may have an arbitrary number of vertices with none, one, or more edges connecting some or all of the vertices. If you have "V" vertices and "E" edges, how many structurally different graphs can be constructed?
     Ramanujan Numbers
Ramanujan Numbers and the Taxicab Problem. The simplest of these solution groups is: 1^3 + 12^3 = 9^3 + 10^3 = 1729. Includes graphs showing 2-way, 3-way, 4-way, and the 193 known 5-way solutions. 24,153,319,581,254,312,065,344 has been confirmed as Taxicab(6)
     Analysis of Sorting Algorithms
A common task for computers is to sort data as an aid to analyzing it. Time trials and source code are provided for: Bubble Sort, Insertion Sort, Median-of-three Quicksort, Multiple Link List Sort, and Shell Sort.
     The search for a counterexample to Beal's Conjecture
Does the equation:
Ax + By = Cz
have any solution where:
1) A, B, C, are positive integers
2) x, y, z are positive integers  > 2
3) and A, B, C have no common factor?
If you can answer the above question (with either a “Yes” or a “No”), the American Mathematical Society has a $1,000,000 prize waiting for you.
Bad News - there's no counterexample up through Cz <= 1.0E22 (and counting).
      Magic Squares
Magic Squares exist for many different sizes and may have various qualifications on the numbers they contain. We will look at simple 3x3 Magic Squares and take a brief look at the “3x3 Magic Square of Squares” problem.
 Applied Mathematics
     Guaranteed Profits in Stock Market Options?
This is a demo model illustrating how a linear programming system can be used to find an optimal profit for arbitrage positions in stock options.
     Mega Millions Odds & how to calculate them
In addition to the published odds for the Mega Millions Lottery Game, the mathematics on how to calculate these odds is also shown.
     Powerball Odds and how to calculate them
The standard odds, probabilities for multiple winners,  calculations for “Power Play Multiplier”, and expected “Return on investment” are all included as well as the math operations that are used to calculate these numbers.

Global Warming - and those people with closed minds that blindly deny it
“The Great Global Warming Swindle” is itself a Fraud and a Swindle
 “The Great Global Warming Swindle” is a pseudo-documentary in which British television producer Martin Durkin has fraudulently misrepresented both the data involved and scientists who have researched global climate. Movie director Durkin has willfully misrepresented the facts about global warming just to advocate his own agenda.
    Global Warming Denial - Liars
Global Warming Deniers misrepresent the scientific facts of Global Warming / Climate Change in multiple ways. The misrepresentations can take the form of paid political propaganda, ignorance, outright lies, etc. The people responsible for these misrepresentations can vary from “think tanks” and lobbyists that are financed by large corporations down to ignorant individuals. In particular: The Oregon Institute of Science and Medicine is in reality - a farm, and Christopher Monckton - A vociferous Global Warming Denier Liar.
    Roger Cohen’s proposed $5,000 bet
A (retired) Exxon Mobil executive’s attempt to use money to promote his personal agenda. (Which is to deny “Global Warming”.)
    The “Global Warming Stopped in 1998” Lie
One of the false claims that Global Warming Deniers have been making in recent years is that “Global Warming Stopped in 1998”. As per usual, this claim is another deliberate GWD falsehood that can be easily debunked by looking at the actual observations.
The Fabius Maximus Website is an example of a Global Warming Denier website. A look at the evidence that GWDs lie, they are willfully ignorant, and they are wrong.

Fight DMCA Abuse

     How to fight back against DMCA abuse
The Digital Millennium Copyright Act has been used abusively to suppress legitimate criticism of cultists and other “questionable activities”. Here’s an outline on how to fight back if you are ever a victim of a DMCA attack.

Fee Demo
    Fee Demo Complaint
U. S. National Forests are a national responsibility - illustrated with a Beetle Bailey cartoon.  We now have to pay additional fees to access our National Forest lands. This is in addition to the federal taxes that we all pay. Previously this tax money was used for maintenance of these publicly owned lands.

Animas River Flood
The winter of 2004/2005 had a much above normal snow-pack over the San Juan Mountains. A heat wave in mid/late May melted large amounts of it all at once.

A Giant Sequoia grove near Durango, Colorado
A log  of the author's effort (and a general “How to” guide) to get a Giant Sequoia grove to grow next to the author's home west of Durango, Colorado

A complaint about a poorly designed Chippendale Curio Cabinet as advertised and sold by Amazon.com.
It's beginning to look like a lot of people (including Amazon) are the victim of Visiondecor Furniture.

A complaint about what I believe are the fraudulent sales practices of RXShoppers and Quickneasypay

Website Hits
    Over 5.0 million page hits since start-up March 13, 2001.
    The pages most frequently visited are (some variation with time):
“The Great Global Warming Swindle” is itself a Fraud and a Swindle
Powerball (Visits increase sharply when large jackpots exist)
Mega Millions (Visits increase sharply when large jackpots exist)
Home page
Evolution of the Colorado River
(Parker Brothers) Monopoly
Grand Canyon Tour
N_Queens (A surprisingly popular classic puzzle)
Creationism (& related pages)

Web page generated via KompoZer

Information About the Website Author
     Bill Butler
     E-mail: lisabill@wcenturywlink.net  (Remove both "w"s for a valid E-mail address.)

The author's home near Durango, CO

The photo above shows the author’s home near Durango, CO. For a 4 minute aerial video, please see

(Click on the full screen icon in the lower right corner for best resolution.)

Note: The author (Bill Butler) of this website is a magna cum laude, Computer Science graduate of Brown University. A brief bio can be found at message # 8 http://groups.yahoo.com/group/CSAtrium/
(CSAtrium is a Yahoo group for the “alums of Brown University’s Computer Science Department and Computer Engineering graduates”.)