An astute reader recently brought to my attention the nascent movement afoot to replace π in common usage with the number now unfortunately known as 2π—viz., 6;349419 (dec. 6.283186):

• Pi Is Wrong! - By Bob Palais
• The Tau Manifesto - By Michael Hartl

(For a reasonably convincing argument on why the letter τ (tau) in particular should be adopted for this value, please read Mr. Hartl's manifesto.)

The fundamental point here is that, in trigonometry and all other manner of angle-measuring endeavors, what we care about is the radius of a circle, not its diameter. The one follows from the other to be sure, but at the end of the day the diameter is more usefully considered twice the radius than the radius is half the diameter. A circle is a circumference around a center—it is the measure of this distance between center and circumference that is elemental to the idea of a circle, not the rather incidental fact that its full width is twice that same distance. Read more »

Anyone following the hexagonal news of late has no doubt noticed a flurry of stories related to the upcoming release of Civilization V, and in particular its new hexagonal tile system. In this blog's opinion, the adoption of hexagonal tiles by the Civ franchise is a long overdue development, and frankly one that should've been incorporated into at least the last two Civ releases. Indeed, many DOS-based strategy games have used hexagonal tiles going back to the late '80s, and one has to wonder why Civilization ever used square tiles. (I remember playing the original Civilization in the early '90s, well before the advent of my own hexagonal illumination, and thinking that, in fact, it would be better with a hexagonal grid. I can only imagine part of the media excitement here—aside from just the general awesomeness of hexagons—is due to the fact that many, many other people have had the exact same thought over the past twenty years.) Read more »

I have been reading about the PAH world hypothesis, and have come to see it as an intriguing indicator of the potentially hexagonal origins of life on earth.

Essentially, it is conjectured that, since polycyclic aromatic hydrocarbons are among the most common spaceborne molecules in the known universe, they would have likely been a constituent in the primordial seas of Earth, where they could have provided some sort of scaffolding or template on which early biological polymers such as RNA could assemble, thus solving a frequently-raised objection to the RNA world hypothesis that RNA is too fragile and transient to survive long outside of an extant cell or similar protective environment. By providing a structural backbone on which reasonably complex RNA strands and such could self-assemble, the PAH world would have given early pre-cellular life a fighting chance of finding its way into protective lipid bubbles, weird mineral formations, or what have you, where given enough replicative iterations it presumably developed into proper cellular life as we know it. Read more »

It looks like the hexagonal zeitgeist is finally floating to the surface of our collective media environment. Two stories in particular off of our hexagonal news feed caught my eye this morn:

Geometry lessons
". . . Just as the 1950s will always be remembered as the decade of atomic-inspired motifs, so may the early decades of the 21st century be remembered, by those of pop cultural bent, as belonging to the hexagon."

The Hexagon Harley 1.4301
"Six is the magic number on this handcrafted custom Harley Davidson by Horst Dzhangmen. Everything but the engine, a HD Shovelhead 1340 cm3 and the frame, has been cut and built into perfectly shaped hexagons and this exceptional work took its creator three years of hard work to achieve this perfection."
Read more »

This site is not yet completed, and at least one core content piece is still in progress, but after some months halfassery, I am prepared at this time to move into Phase I of my three-phase site launch program. This site is live as of May 30, 2010 (May 26, 11B6), and hopefully shall remain so. FTVW.

Again, I cannot overemphasize how not-ready-for-formal-launch this site is. Structurally, several site elements still need some work, and as I said some content is still being developed, including my short mathematical summary of hexagons, which, though somewhat trivial, arguably constitutes a somewhat significant piece of content on a site nominally about hexagons.

Hopefully we will be ready to proceed to Phase II within the next week. Thank you.

This is old but worth considering:

• Is the universe a dodecahedron?
• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background

I have been completely unable to find any sort of followup to this since 2003. The whole idea may have been discarded by now, I'm not sure, but considering that Plato speculated—for no particular reason modern science is aware of—that the universe was shaped like a dodecahedron nigh doz. 1,500 years ago, this is obviously a significant conjecture to put forward.

While the other four platonic solids have traditionally been associated with the four classical elements, the dodecahedron has been identified with the universe, or the aether. Did the ancients have some insight into the cosmological structure of our universe that we are only rediscovering now? Maybe! Or maybe the whole idea is crap. Who knows! But the hexagonal implications are obvious—twelve being a multiple of six, the twelve faces of the dodecahedron forming six symmetrical pairs, et cetera.

I am hopeful that eventually more data from WMAP or its successors will shed further light on this hypothesis.