I jog each Sunday at some time between 7am and 11am. I’d been immensely surprised that the jogging since January has not decreased my energy during the rest of the day - up until now. In fact, prior to today, I was happy to feel full of energy for the whole of each Sunday. When I’d taken to jogging in the distant past I always found I had a jogging “high” for about an hour afterwards and then felt a slump in energy - perhaps even sleepiness.

Today, however, was different. It may be unrelated to the jogging, but I was definitely extremely tired in the late afternoon and I still feel pretty tired now at about 9pm. It may be other factors or it may be that the distance has become significant enough to cause noticeable fatigue. I suppose I shall just have to see what happens during the coming weeks.

Nevertheless, from a mental and spiritual perspective, the jogging is proving to be a wonderful habit. The act of jogging has itself become meditative. I find myself contemplating my future - in a very positive frame of mind - thinking thoughts (some might say prayers) of gratitude and enjoying the changing surroundings. I even found myself - entirely unintentionally - delivering a speech!

As I have resigned from my teaching post (officially as of the end of August, but in all important respects at the end of the Summer term), I will be expected to give a farewell speech to the entire school in the year’s end assembly. Pretty much all staff and pupils are present and it could seem a daunting occasion.

I was amazed at my own eloquence and humour as I delivered this speech to myself (without any prior rehearsal and without any forethought whatsoever). I can scarcely imagine I will be so eloquent on the actual occasion, but if I continue to spontaneously rehearse during my Sunday jogs, who knows?

Given that I’d like to become a better public speaker, I think my jogging could provide a great opportunity to play things through in my head.

In general, I have been amazed at the clarity of my thoughts while jogging. The very act of jogging and the affirmations I recite from time to time during the jog induce a heightened state of positivity. Consequently, I have a lot of interesting thoughts and ideas that I only wish I could retain and come back to later. I think I could use some kind of dictaphone to record some of my thoughts. . .

On a related note, I’ve found a couple of GoogleMap-based websites that allow me to create jogging routes (essentially for the purposes of seeing how far I’ve run). I’m beginning to test these out, but I’m not sure editing previous routes is particularly easy to do. Given that I’m adding more and more diversions to the middle of my route to increase its length, I’d like to be able to insert new waypoints to (or delete old ones in) the middle of a route but I’m not sure if I can do this. The utilities I’ve found so far only appear to enable me to delete points from (and add points to) the end of a previous route.

I’ll hopefully link to the two jogging route utilities I’ve found in the next entry.

As it turns out, the toy has proved far more intriguing to me (and other adult visitors) than it has to my children! It’s flexibility allows it to mutate between an equilateral triangular shape and a 3D framework (where its six component pieces form half of the 12 edges of a cube).

Purely for the intellectual and creative challenge, I set out to produce an animation of the metamorphosis from equilateral triangle to cube-frame. My eventual success surprised even me. I intend to make some further refinements but the current result is shown below. [Do not adjust your speakers. I have yet to attempt to add any kind of soundtrack to the animation as yet!]

These ideas were then used to create more realistic images in POVray (a FREE ray-tracing program that allows complex 3D forms to be created by amalgamating mathematical objects in various ways ). Whilst this particular animation is mathematically complex, it is incredibly simple to produce some impressive objects in POVray and animate them in all manner of ways. The interested reader is welcome to inquire further but is advised that POVray is an enjoyable but time-consuming hobby!

Multiple freeze-frame images from POVray were then compiled using Windows Movie Maker (which I presume is part of the Microsoft Windows package as I certainly didn’t purchase it specifically).

The mathematically-minded reader is invited to solve the following problem:

If the length of each of the six components is considered to be 1 unit (and for simplicity we are measuring each component from the centre of one hinge to the centre of the hinge at the other end):

1. What is the distance from the centre of the red-blue hinge to the centre of the green-yellow hinge when the model is in the equilateral triangle formation?
2. What is the distance from the centre of the red-blue hinge to the centre of the green-yellow hinge when the model is in the cube-frame formation?
3. What happens to this distance as the model is flexed?

I have yet to answer the third question, but the answers to the first two questions have led me to an intriguing (but seemingly improbable) conjecture that I’ve yet to prove or disprove. I would be very pleased and impressed if anybody can confirm my results for questions 1 and 2, guess at my conjecture and help me out in any way with question 3!