Tag Archives: Online Articles

Fitness with the Tortoise and the Hare

Does Aesop’s fable, The Tortoise and the Hare, actually teach us about fitness and how to pace your run? Maybe not, but it helped me put an insight into perspective in “The Tortoise and Hare Approach to Running Pace“, my latest DeHaan Fitness post.

"Rabbit foraging in Alabama" image by Stephen Kirkpatrick, USDA Natural Resources Conservation Service
"Rabbit foraging in Alabama" image by Stephen Kirkpatrick, USDA Natural Resources Conservation Service

Okay, Aesop Really Didn’t Say Much about Fitness

I’d like to feel as quick as this rabbit, but as I admit in that blog post, I felt really slow at the start of that fitness session.

And no, Aesop truly did not discuss “pace” for exercising. He had a different insight about competition. Actually my blog post is about setting a wise pace early in the run. I used the “Tortoise and Hare” phrase to highlight the contrast between trying too hard versus starting with a sustainable pace.

Two Sources for Aesop’s Fables

I found a couple of good Kindle books of Aesop’s fables, in Amazon. Read them for Aesop’s wisdom on a range of subjects… or to give your children something to dream about.

Aesop’s Fables (Kindle Edition)” has a low price, and a 4-star rating from 7 reviewers. Each modernized fable has its own illustration. Check it out in the Canadian edition or the American edition.

The “Aesop’s Fables (Oxford World’s Classics – Kindle Edition)” version has a whopping 600 fables! The only review gives it 5 stars. This version has been translated anew from the Greek. It’s recommended for the parent who wants to know what the original stories really said. Check it out in the Canadian edition or the American edition.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy, DeHaan Fitness, and other sites. I also promote my articles with writing tips in my Blog of Writing site: for example, “One Writing Tip from Running with Aesop“. That’s why we highlight these online articles on this blog page.

To only see Toronto events, or only the fitness articles, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin.

Disclaimer: The information contained in these articles is for educational purposes only and should not be used for diagnosis or to guide treatment without the opinion of a health professional. Any reader who is concerned about his or her health should contact a doctor for advice.

Previewing One Example of Applied Geometry

(Updated Jan. 7, 2015) We finally published “Green Math: How to Apply Geometry to a Square Foot Garden” in Decoded Plants. Perhaps I was right to highlight these images. The editor rejected my adaptation of Toby Hudson’s circles, but hand-crafted some original art in its place. As well, fellow writer Chris Eirschele kindly offered several images of actual container gardens to show what one can do within a limited plot of land. Finally, I didn’t even include the “square root of 2” image, since it didn’t really add that much for a gardening perspective.

Here’s a preview of images I made for an upcoming article about applied geometry. Now that my article is published, I’ve shared the link and further details. (End of update).

Why preview these images? The act of publishing them first on my own online site establishes copyright.

Packing Many Circles into a Square

"Pack Circles into Squares". Copyright image by Mike DeHaan based on original work by Toby Hudson @ http://commons.wikimedia.org/wiki/File:Circles_packed_in_square_2.svg .
“Pack Circles into Squares”. Copyright image by Mike DeHaan based on original work by Toby Hudson @ http://commons.wikimedia.org/wiki/File:Circles_packed_in_square_2.svg .

Most of the work was done by Toby Hudson, who published it online under a Creative Commons license. My work was to capture a screen-print of all these images, and then crop the image and add a border. Hopefully the finished article will show it as a larger image so it will be easier to read.

Perhaps it’s obvious that my article will focus on how to pack circles into a unit square as efficiently as possible.

Pythagorean Theorem for an Isosceles Triangle

"Square Root of Two in Square Foot Garden by Pythagorean Theorem" image by Mike DeHaan
“Square Root of Two in Square Foot Garden by Pythagorean Theorem” image by Mike DeHaan

I drew this image in MS Paint to illustrate a 1-1-root(2) triangle. Per the Pythagorean Theorem, the length of the longest side is the square root of the sum of the squares of the other two sides.

Since the outside edges of the square have a length of “1 unit”, the diagonal of the square is the hypoteneuse of a 1-1-√2 right-angle isosceles triangle.

The Pythagorean Theorem says that hyp^2 = side_one^2 + side_two^2. Since each side has length of 1, hyp^2 = 1 +  1 = 2. So the length of the hypoteneuse = the square root of 2 = √2, or about 1.4.

Red Circles Do Not Quite Fit Inside the Square

"3 Circles Too Large for a Unit Square". Copyright image by Mike DeHaan.
“3 Circles Too Large for a Unit Square”. Copyright image by Mike DeHaan.

I wanted to fit three circles along the diagonal of this square. They fit along the diagonal, but bulge out beyond the sides of the square.

Obviously the circles did not fit perfectly along the diagonal either. I had converted the unit square from feet to inches, because the article is mainly aimed at readers in the USA. The square root calculation rounded more closely to 5.6 inches, so I rounded down to 5½. The red circles would have bulged out even more had I been more careful with the fraction-of-an-inch!

I used MS Paint to crop these images and add a border. At first, I’d forgotten to doctor the image after moving it from the camera to my computer. I was surprised that the original image of the green circles was “too large” to be uploaded to this site; but it had accepted the original red circle image.

I could have changed the WordPress parameters for my site, to allow larger images. However, I would have cropped them both anyway. There was just no need to include so much of the “landscape” that the camera captured.

Green Circles Fit the Square

"3 Circles Fitting into a Unit Square". Copyright image by Mike DeHaan.These green circles do indeed fit inside the square. Unfortunately, they don’t reach to the corners of the square.

I wonder whether that will become a sore point with the readers who want to apply this geometry to their practical situation. Perhaps there will be feedback for that article.

Learn from the Father of Square Foot Gardening

Mel Bartholomew has not just “written the book”, he’s written several books on Square Foot Gardening. You should read the Kindle edition of “All New Square Foot Gardening, Second Edition: The Revolutionary Way to Grow More In Less Space“, available from Amazon in Canada and from Amazon in the USA.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, and other Decoded sites. That’s why we highlight these online articles on this blog page.

I also publicize many of my articles in another blog; read “Geometry Applied to Square Foot Gardening” for a writing tip.

Thank you for reading this preview of applied geometry.

How to Avoid Envy when Dividing the Spoils

Do you need to divide your inheritance with a sibling, or your property as part of your divorce?

My recent Decoded Science article, “How to Divide Indivisible Goods Fairly: Algorithm for Dividing Assets“, explains how to use one specific process of “dividing the spoils” between two parties, that avoids either party envying the other.

Three university professors collaborated to develop this algorithm, and to prove mathematically that it gives one of the best possible results if you want:

  • Each party will receive the same number of items.
  • Afterwards, when each party reviews who got what, paired in their own order of preference, then each party prefers his own first, second, third (and so on) item to the one the other party received.
  • Keep each item whole; do not divide any item into pieces, or sell it to divide the monetary value.
  • You can accept that some items will go to a “Contested List” rather than to either of the two parties.

I also made some spreadsheets to illustrate what the process might do to divide assets when inheriting an estate or negotiating a divorce.

"Allocation Results Example 2" : Image by Mike DeHaan
“Allocation Results Example 2” : Image by Mike DeHaan

Canadian Content for a Fair Division of Goods

I also had a brief e-mail interview with Dr. Marc Kilgour, a professor of mathematics at Wilfrid Laurier University in Waterloo, Ontario, Canada. He’s one of the authors of the underlying paper with the algorithm. One tidbit that didn’t get into my article, is that Canada’s NSERC (Natural Sciences and Engineering Research Council) provided a grant which partially funded this “curiosity-driven research”.

If You Don’t Have an App for That…

Even though their algorithm might not have been incorporated into a computer program or smartphone app (yet), you might still benefit from this research.

Ask your divorce mediator or estate planner to guide you through the steps outlined in the original research paper. There’s no guarantee that it will resolve all the items, but it can simplify the task of avoiding envy when dividing the spoils.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy, and DeHaan Fitness. That’s why we highlight these online articles on this blog page. I also add writing tips to my promotional posts in my Blog of Writing; see “Preview of Dividing Indivisible Goods Fairly” for an example.

To only see our Toronto events (for things to do in Toronto) or fitness articles, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin.

Thank you for reading my online articles about avoiding envy when dividing goods fairly.

Disclaimer: The information contained in this article is for educational purposes only and should not be used to guide your decisions without the benefit of professional advice. Any reader involved in property disputes or settlements should consult an appropriate professional.