Curvature of loxodromes

Paths of constant bearing (known as ‘loxodromes’ or ‘rhumb lines’) are often mentioned in the context of the Mercator projection, as they are always straight lines on the map. It’s often emphasised that this is not the shortest route between two locations, but something I feel is glossed over is the direct consequence that these paths are not straight on a sphere, even though the bearing is consistent. In general, following a steady course on a compass requires turning slightly along the entire journey. Perhaps the most obvious indication of this is to imagine travelling due east when only …

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Mundane number golf

There was an online discussion regarding ‘magic numbers’ in software – numeric constants serving an important role with no description or justification for their value – and one static analysis tool’s assertion that the only numeric constants permissible in statements are -1, 0, and 1. Although the significance of undocumented numbers in written software is often not readily apparent, sometimes the function of a number really is nothing beyond its literal value, and this sort of overzealous rule is guaranteed to complain about expressions whose intent actually is readily apparent – but none of that actually matters because someone soon ported the …

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The small-circle equidistant projection

It’s a simple fact of life that everyone loves the azimuthal equidistant projection, which shows the world at the correct distance and direction from its central point, even those who have never seen the term in their life.

For example, when centred on Sydney:

Azimuthal equidistant map centred on south-eastern Australia, showing the world in rings up to 20000 km away

One particular point of interest is that Cuba is shown east of Sydney, despite being in opposite hemispheres. And while this is literally true…

A geodesic running from south-eastern Australia at a 90° bearing, ending in Cuba 14883 km later

It doesn’t do much to affirm ill-conceived views of the world perpetuated by cylindrical and pseudocylindrical maps. Wouldn’t it be nice to use terrible metrics for ‘distance’ and ‘direction …

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2024 artober roundup

Last year I said, “Last year was nice and all, but […] if part of the goal is to practise then next time I should do something more in line with my typical approach.” The same held true this year, so this time I went for full colour and abandoned any remaining semblance of ‘Inktober’ beyond lifting the prompts. Except I didn’t really have time for daily drawings and haven’t generally enjoyed the experience of finding something for prompts that don’t inspire, so this time I decided from the outset that if I didn’t have time or …

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Alternatives to the ‘Antarctic ice wall’

Everyone loves the azimuthal equidistant projection; some just don’t yet realise it. For that latter camp, a quick refresher: azimuthal equidistant maps show all courses from the centre point at the appropriate angle and with correct scale – a ray from the centre to any point shows the initial bearing and length of the direct route to that point. The azimuthal equidistant projection, which unfortunately lacks a more concise name (‘Postel’?), is quite popular with some rather diverse groups, including the contemporary ‘zero-Gaussian-curvature Earth’[1] crowd. Perhaps more perplexing than this movement’s modern resurgence, is their insistance on the …

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Magnetic field of the Earth

One of the labours of Hercules was surely to find a map of Earth’s magnetic field.

There’s no shortage of crude diagrams of bar magnets superimposed over cartoon globes, and plentiful plots of isogonic lines to be procured from multiple perspectives; yet for accurate depictions of the simple lines of magnetism over Earth’s surface, the offerings seem sorely slack. So just imagine how hard that would have been two thousand years before the internet.

The most common chart I see that has an actual connection to reality, is a map of isogonic lines – contours of equal magnetic …

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The origin of oxygen

There’s a bit of a persistent rumour getting around on internet and extranet circles. Actually far too many, but today’s lucky topic is the notion that plants produce oxygen from carbon dioxide.

It’s a simple enough story. We know that photosynthesis consumes carbon dioxide, and produces surplus oxygen. Since CO₂ quite obviously contains O₂, well, there’s not even anything to question.

Except that photosynthesis has a few more aspects than just these two gases, and the whole system isn’t an atomic process.[1] Fortunately you don’t need to be within arm’s reach of …

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The packaging hypothesis

Let’s suppose you have a box. Ideally this is no mere supposition but you actually have a box nearby right now. If you don’t, you’ve surely had one at some point, so in that case we’ll talk about that box.

Boxes are made for storing things. You can put all sorts of things inside your box. You could even put another box inside it.

And you needn’t stop there. Another box can go inside your boxed box, or you could even put multiple boxes alongside each other inside the original box. All manner of boxes …

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