# DeHaan at Decoded Science

This is simply a chronological hyperlink list of Mike DeHaan’s articles at Decoded Science, starting with the oldest.

(Return to the directory of all the sites for which I have written articles).

“Counting Change” by °Florian

## Mike DeHaan’s Articles at Decoded Science

1. The Tesseract: Folding and Unfolding a Simple 4D Hypercube in “Mathematics”
2. Brief Survey of the Health Benefits of Curcumin in “Health”
3. Introducing the Fibonacci Sequence in “Mathematics”
4. Introducing the Golden Ratio in “Mathematics”
5. How to Change Triangular Numbers into Square Numbers in “Mathematics”
6. The Proof and Practice of Thales’ Theorem for Circled Triangles in “Mathematics”
7. A Quick Explanation of Mathematical Induction in “Mathematics”
8. Collatz Conjecture Remains Unproven Despite its Easy Arithmetic in “Mathematics”
9. The Surprising “Benford Law” of Leading Digits in “Mathematics”
10. Zeno’s Paradox of Achilles and the Tortoise in “Mathematics”
11. From the Cartesian Plane to the Areas of Rectangles and Triangles in “Mathematics”
12. How to Find Limits of Mathematical Functions in “Mathematics”
13. Differential Calculus Introduction: Simple Polynomial Equations in “Mathematics”
14. Starting Integral Calculus by the Summation of Riemann Integrals in “Mathematics”
15. L’Hopital’s Rule is a Hospital to Cure Ailing Functions in “Mathematics”
16. The Leidenfrost Effect is a Simple Home Science Experiment in “Laboratory”
17. Solve the Monty Hall Problem using Logic and Mathematics in “Mathematics”
18. Variations on the Coffee Ring Home Lab Experiment in “Laboratory”
19. Is the Elevator Puzzle a Math Paradox or a Paranoid Delusion? in “Mathematics”
20. The Paradox of the Infinite Series of Square Numbers by Galileo in “Mathematics”
21. Cantor Defeated Galileo in the Battle of Infinite Numbers in “Mathematics”
22. The Square Root of Two is a Real Irrational Number in “Mathematics”
23. Lightning Fast Math for Neutrinos versus the Speed of Light in “Mathematics”
24. A Quick Reference Guide to the Set of Natural Numbers in “Mathematics”
25. A Guide from Natural to Imaginary and Infinite Numbers in “Mathematics”
26. Motivate Repulsive Grapes with Neodymium Magnets in “Laboratory”
27. The Definitive Quick Reference Guide to All Types of Numbers in “Mathematics”: this is the complete guide
28. A Brief Introduction to Prime Numbers in “Mathematics”
29. Filtering Prime Numbers using the Sieve of Eratosthenes in “Mathematics”__”Math Theory”
30. Several Different Paths to Prime Numbers in “Mathematics”__”Math Theory”
31. The Complex Tale of Eisenstein Prime Numbers in “Mathematics”__”Math Theory”
32. Four Personalized Prime Number Formulae  in “Mathematics”
33. Power Sets come in Small, Infinite and Even Larger Sizes in “Mathematics”__”Math Theory”
34. Introducing Probability Theory without Statistics starts a new series in “Mathematics”__”Math Theory”
35. The Probability of the Allais Paradox in Lottery Preferences  in “Mathematics”__”Math Theory”
36. Axioms and Two Useful Theorems of Discrete Probability Functions in “Mathematics”__”Math Theory”
37. A Taste of the 2012 Joint Mathematics Awards and Prizes in both “Headlines” and “Mathematics”
38. An Introduction to Conditional Probability in Mathematics in “Mathematics”__”Math Theory”
39. The Pitfall that Conditional Probability is Not Commutative in “Mathematics”__”Math Theory”
40. Repercussions from the Richard Paradox in “Mathematics”
41. Potential New Algorithm to Calculate the Cube Root of a Number in “Mathematics”__”Math Theory”
42. A Brief Introduction to the Turing Machine in “Mathematics”__”Math Theory”
43. Examples of Turing Machines: Loops, Halts, and Rewriting in “Mathematics”__”Math Theory”
44. The Special Case of Non-Deterministic Turing Machines in “Mathematics”__”Math Theory”
45. The ACM Awards the 2011 Turing Prize for Computing to Judea Pearl in “Mathematics”
46. The Universal Turing Machine is a Turing Machine Emulator in “Computing”
47. Turing Machines and the Halting Problem in “Mathematics”__”Math Theory”
48. Computer Algorithm Solves Arranged Marriages via the Hall Theorem in “Mathematics”__”Math Theory”
49. How Statistics May Help Select a Reliable Pollster in “Mathematics”__”Calculations”
50. The Turing Machine versus the Decision Problem of Hilbert in “Mathematics”__”Math Theory”
51. T Cells, Predators and Finances all Walk the Levy Walk in “Mathematics”
52. It Would Take a Titanic Raft of Flotsam to Float Two Actors in “Mathematics”__”Calculations”
53. Euclid Laid the Foundations of Geometry in “Theoretical Science”, the new home of “Mathematics”
54. Elements of Geometry: A Brief Guide to the Euclidean Axioms in “Theoretical Science”
55. A Brief Guide to the Euclidean Postulates in “Theoretical Science”
56. One Non-Bayesian Approach to the Two Envelope Paradox” in “Theoretical Science” in “Theoretical Science”__”Mathematics”
57. Introducing Math Symbols for Union and Intersection in”Theoretical Science”__”Mathematics”. This was also a response to an “Ask the Expert” question.
58. Introducing the Factorial, the Exclamation Mark of Math” in”Theoretical Science”__”Mathematics”__”Math Theory”. This begins a series that should lead to permutations, combinations and discrete probability.
59. Trace the Source of a Rumour or Epidemic via its Network” is in both “Theoretical Science”__”Mathematics” and also “Headlines”. A new pair of algorithms can backtrack through a network more efficiently than could its predecessors. How? That’s what my article begins to explain.
60. Population Prediction of More Retirees, Fewer Workers by 2100” discusses a population study for the UN that used Bayesian methods for more accurate prognostication.
61. Introducing the Binomial Coefficient for Positive Integers” continues from article #58, the “Factorial”, with applications to combinatorics and algebra.
62. How to Convert the Base of an Exponent with Logarithms” does what it says on the label. This Decoded Science article provides a formula to convert from a “power of two” to a “power of ten”, while explaining the general principles.
63. H1N1 in Households, or the Math of Spreading Swine Flu” is a headline math article explaining Dr. House’s report on a “u-shaped”, rather than “n-shaped”, Gaussian distribution to model how readily the 2009 swine flu was transmitted in households in one British city.
64. Math can Launch One Bus with Speed minus Gravity” explores the math behind the Speed movie’s bus leaping across a gap in an overhead ramp on a freeway. Would a cannon ball have succeeded?
65. Reliable Pollster Report Card in 2012 Presidential Election” presents a statistical report card to Gallup, Rasmussen and, yes, Nate Silver.
66. A Statistical Method for 2012 Election Vote Fraud Allegations” presents a pro forma analysis of the “108% registration” allegation for Wood County, Ohio.
67. Winning Powerball Tickets in Arizona and Missouri: How to Calculate the (Slim) Odds“, written Nov. 28, 2012, explains how to calculate the astronomically poor probability of winning the powerball jackpot.
68. The Lottery Paradox Versus the Math of Probability” shows how to apply probability theory when the odds of winning a raffle seem to say that absolutely no ticket could possibly win.
69. Did the Temple of Solomon Define Pi in the Bible?” examines a verse that could set the value for π. It also reports on whether any American states have used this Bible verse to legislate a value other than the 3.14159265… approximation.
70. Could Firearms Statistics Support Gun Control after Newtown?” shows some techniques for statistics to argue for or against gun control in the wake of the 2012 school shootings in Newtown, CT…or the many that had come before.
71. Estimating Whether No Two Snowflakes are Alike” uses math and probability to examine how likely it would be for any two snowflakes to be alike.
72. What Are Fractions? Math Vocabulary for Parts of a Whole” begins a series on introductory mathematics.
73. Adding Fractions: Using a Common Denominator” is the follow-up to “What are Fractions…”, although this was my original topic.
74. A Sample Case Study of Math for a Casino Business Proposal” examines some of the mathematics I used to examine the business case for the proposed gambling casino in Toronto.
75. Cross Multiply to Solve Equations with Fractions” continues my series for introductory mathematics. The easy math is solving fractions equations.
76. The Buffon Needle Drop: a Math Activity for Pi Day” is the first of three articles presenting mathematical activities for Pi Day in March. This one is a fun experiment for teams of students; it ends by calculating some easy statistics to determine a value of pi (π).
77. My second Pi Day article is “One Circular Math Activity for Pi Day“. Students take measurements and do simple calculations to approximate the value of pi.
78. We wrap Pi Day with “Roll Out the Simplest Mathematics Activity for Pi Day“. Once again the students measure and calculate an approximation for pi.
79. Faster and cheaper but still reliable indicator of “epidemic or just isolated animal-to-human transmission” of influenza or other diseases uses statistical math. My breaking news article on March 5, 2013 is “Math may Distinguish Flukes from Flu Epidemic Outbreaks“.
80. How to Make a Natural Number Series of Square Numbers” responds to a reader’s question about calculating a number series of square numbers without just multiplying a number by itself. Yes, there are some tricks up the proverbial sliderule.
81. Mythbusters Math to Compute G Forces from Falling in Bubble Wrap” simplifies the math to calculate the g forces, and why the bubble wrap didn’t save Buster.
82. The Circled Square Math Problem Claims Pi Equals Four” is the answer to a friendly troll’s puzzle.
83. Cancer Research Applies a Markov Chain Monte Carlo Approach” isn’t gambling with oncology; rather it helps predict where a tumour might colonize.
84. How to Calculate Simple Interest” introduces the simple interest formula.
85. How to Calculate Compound Interest” is the obvious follow-up to “Simple Interest”.
86. How to Find Pythagorean Dates for Any Year“. Be the first to circle the next Pythagorean date on your calendar with this handy how-to guide.
87. The Drake Equation Estimated the Scope of the SETI Project” explains how the Drake Equation predicts how many alien civilizations the SETI Institute might detect; and how other approaches would need different equations for their projects.
88. In response to an “Ask an expert” question, “Risk Assessment for Skydiving versus Grocery Shopping” compares mortality rates for parachute jumping versus going to the grocery store.
89. In October, I wrote “Hypatia Taught Conic Sections and Diophantine Equations” when a colleague wrote about her, but without the math, in Decoded Past.
90. The next day, the editor asked for “Interpreting One Report of Statistics on Science Comprehension“, in which we review a professor’s surprising study of how well Tea Party supporters comprehend science, versus people of other political stripes.
91. Free Will, Determinism and Turing’s Halting Problem” reviews and, dare I say, adds to MIT Prof. Seth Lloyd’s application of Turing’s Halting Problem to the question of free will versus determinism.
92. After a few months hiatus, I managed four articles in October, ending with “How Modal Logic Proved Godel was Right, and God Exists“. Kurt Gödel’s theorem proves God exists; and computers have verified Gödel’s logic.
93. I wrote “Practical Uses of Matrix Mathematics” on Dec. 17, 2013 in response to a reader’s question about day by day uses for matrix arithmetic.
94. Another reader’s question led to “Risks of a School Shooting versus an Airplane Crash” on Dec. 27th.
95. The editor suggested another “mass shooting” topic, so “Trending Statistics for Major Fatal US Shootings” was published Jan. 28, 2014.
96. Almost a month later, I wrote “How to Divide Indivisible Goods Fairly: Algorithm for Dividing Assets” which includes a micro-interview with one of the three authors, who works at a Canadian university.
97. Comparing the Genetic Code of DNA to Binary Code” was my first article at Decoded Science in over a year. Earlier in August 2015, another Dec.Sci. writer had posed this question on Facebook; I took it as a challenge.
98. Soon afterwards, I wrote “Detecting or Avoiding the Yule-Simpson Paradox” which deals with the situation wherein a trend found in partitioned subpopulations is reversed in the overall population. Believe me, it’s easier to understand with the first example.
99. My Decoded Science article for October was “Introduction to Bayesian Probability and Bayes Theorem“, and should be the first of three.

Here’s my Decoded Science author page.

### Recommended Online Math Reference

I’ve used MathWorld–A Wolfram Web Resource for many of my mathematics articles. It’s not the only source, but it’s a very good one.

As an example, for any of my articles about conditional probability, I referred to:

Weisstein, Eric W. “Conditional Probability”. MathWorld–A Wolfram Web Resource.

## Decoded Science added the LaTeX Plug-in

The LaTeX plug-in allows a string of code such as

$\displaystyle \mathop{\mathbb E}_{x\sim X} f(x):= 1 \ \ \ (1)$

to be rendered as

$\displaystyle \mathop{\mathbb E}_{x\sim X} f(x):= 1 \ \ \ \ (1)$

Yes, this does indeed work here in the DeHaan Directory.