Conic Section

 Children often ask their maths teacher when they'll use what they're being taught. For me it's so that I can waste a huge proportion of my weekend worrying about concepts that have already been explored centuries ago.

Inside you there are two wolves. One wolf sees interesting maths problems in everyday life. The other wolf likes solving maths problems.

I'm currently down a worse rabbit hole than recognising bad kerning https://xkcd.com/1015/ There are many things that artists get wrong when they paint the moon and I've learned to spot a load of them. I started wondering what shape the terminator (the line between the light side and the dark side) should be and it got a little out of hand.

The moon is a sphere (to all intents and purposes) and the sun is a point source of light (for all intensive porpoises). What shape does the illuminated section have? The limb (the outside edge) is a semicircle. My contention is that the terminator is another arc but I needed to prove it.

Let's say that the outside edge of the moon is described by 𝑥² + 𝑦² = 1

(yes, the coordinate system of my painting is based on the plane of the ecliptic). Let's say that the sun and the painter are looking at the moon from 60° apart so the terminator will be half way between the limb and the centre line. I know that the 1/2 seems arbitrary but if the maths works out I'll go back and replace it with a Greek letter. This will be true all the way up and down the moon because horizontal slices of the moon are all circles, they're all similar, just different sizes. So the question becomes what curve is half way between 𝑥² + 𝑦² = 1 and the vertical line 𝑥 = 0 ?

𝑥₁ = 𝑥⁄2
𝑥 = 2𝑥₁
𝑥² + 𝑦² = 1
(2𝑥₁)² + 𝑦² = 1
4𝑥₁² + 𝑦² = 1

Does that look like it describes a circle? No it doesn't, that's something to do with an ellipse. An ellipse! Hardly are those words out when an image out of maths books troubles my sight. If the moon is a peeled orange (you don't get poetic metaphor like that from amateurs like Yeats and Tennyson) the terminator is the shape of one of the segment lines and they're circles around the orange but angled towards us somewhat.That's the same as saying it's the shape made by cutting a cylinder at an angle and that's the same as saying it's the shape made by cutting a cone at an angle and that's the same as saying it's an ellipse.

So to do the terminator on a moon in your painting you'd seem to need to trace round an ice-cream cone that's been cut off at an angle. Or a traffic cone for larger works.

Richard "There's a Bad Moon on the Rise" B

Bedford Autodrome

 You and I are not the same.

I went on a track day with my boss. It's a long, hot and tiring day and by the end of it we were both tired and sweaty and our hair was moulded to our crash helmets. He magically produced a clean freshly ironed shirt. I did not. He untousled his hair. I did not. He put on good quality sunglasses to keep the sun out of his eyes. I put on a frayed and faded baseball cap to keep the sun out of my eyes.Ninety minutes later we arrived at our motel and sadly there was a mirror in reception. During the drive he had seemingly been further restored while I had continued to wilt.

When we checked in he looked like a stylish and successful gent. I looked like an elderly and frail vagrant who would need to be disinfected and washed before he was allowed into the restaurant.

Richard "quick shower" B

Film Review

At the weekend I saw The Odyssey in the cinema and (like book Odysseus) I have the hubris to assume you might be interested to hear what I thought of it.

Not much. It's not terrible. The best I can say is that it's three hours long and I wasn't bored. William Shakespeare seems to have been able to review the film more than four hundred years before it was made. "It is a tale told by an idiot, full of sound and fury, signifying nothing".

It's a Chrisopher Nolan film so the sound should be bad, but in this case it's abhorrent. He also seems to have misunderstood who Odysseus was, but I think I know why. I very much like the idea that at some point some papers got muddled up between a beverage company planning a restaurant guide and a tyre company getting in to racing. We now have the Red Bull racing team and the Michelin restaurant guide (joke courtesy of https://xkcd.com/3269/)

A few years ago Nolan worked on Barbie Oppenheimer about the father of the atomic bomb. I suspect that some of his research notes from Oppenheimer got muddled in with the Odyssey because in the film Odysseus is riddled with guilt and regret, whereas he should have been boasting about being the craftiest general ever. It's his hubris and boasting that gets him cursed by Poseidon and makes the whole journey back to Ithaca rather arduous.

The gods, the sex, the beauty and the colour are missing from the film, so it seems like a very boring world for a fantastical story.

Richard "Scouring of the Shire Suitors" B

Sometimes a Cigar is Just a Cigar

I recently said that I was disappointed with the effectiveness of my popcorn cannon. One of my friends suggested that the problem might be the moisture content of the kernels, and I think she might be right.

I've now got yet another project I never wanted. This time running a series of experiments with a popcorn cannon using kernels at different levels of moisture content. I do have a humidor that doesn't get much use, but the hygrometer is broken and the louvred box of damp sponge is missing. I plan to "age" the kernels at different moisture levels in the humidor then try popping them, and keeping records.

Richard "This popcorn tastes like a Romeo y Juilieta Number 3" B

Holiday Plans

I need to stop finding out that new interesting things are possible. I found out recently that a skilled blacksmith can hammer enough energy into a cold piece of mild steel that it will start a fire. As well as all the other things I want to achieve in my lifetime I now want to hammer a piece of steel hard enough and long enough to start a fire. My noodle arms and terrible fitness mean that this will be pretty much impossible.

This weekend I found out that in the 1800s there was a lead mining boom in South Dakota and a lot of Cornish were recruited for their mining experience. The important bit is that you can still buy a Cornish Pasty in South Dakota. Now I'm going to have to find the holiday allowance, money and accommodation to fly to the Dakotas just to buy a pasty.

Richard "to do list" B

My Lobster is too Buttery

 I'd like to say these are "nice problems to have" or "very middle class problems" but I fear the truth is that the problems which beset me are quite unusual. It's my birthday and there have been two disappointments.

I bought myself a popcorn cannon, and while it will support 8 bar and survive an explosive decompression, it takes forever to build pressure and it doesn't actually pop many of the kernels.

On top of that my chiffonier has a silk lined cutlery drawer, which now has a moth infestation.

Richard "I know just how you feel" B