Sunset on Cleeve Common. I'm jealous of people who can take beautiful photos. I manage about one half decent one a year. The is this year's.

It's baking hot. There is plenty of shade in the garden, but the dog decides to lie in full sun. He loves to have warm fur!

Here are a few of then with cowslip seedheads behind and one of hundreds of ox-eye daisies.

#bloomscrolling Peak wisteria

#bloomscrolling The Rosa banksiae we plsnted a few years ago us doung pretty well.

Has anyone got any idea what the top left group of symbols in a lift in a hotel in Malta means? My family has only managed scatalogical explanations. That squiggly thing looks like an 8 on its side, but elsewhere it says the max capacity is 13 persons.

Here's a copy of a copy of a copy of a copy of a copy of a copy

Or even negative!

A demo for your delight.

Here's the calculator I used at school, decorated by the puppy.

@davidkbutler.bsky.social It is a magnificent Autumn for berries here in the UK. Just look at this spindle bush in a field near my home.

That was a close game!

I suspect most pea plants are simply connected. Not this one. Cue other mathematically interesting plant pics.

This supermarket trolley wheel misunderstood the instructions concerning which axis it is supposed to rotate about.

Pray tell me, Dr Fermi, how many flowers do you think there are on my wisteria.

Granddaughter has always loved rainbows. We made a rainbow-themed picnic for her 12th birthday. Note the black things at the end. They represent ultraviolet!

Our fritillaries are very happy by the pond.

Mathematics in School in shreds. Does anyone want a dog?

Looks like I forgot to attach the photo

Now, every point (a,b) on the plane lies on exactly one of these curves, namely the one where λ=f(a,b). So the curves cover the plane, and can do so very prettily. Here's a simple one for a hyperbolas x^2-xy-y^2=λ.

#MathsOnHoliday I'm rather enjoying watching this rotating door. Its circumference has 2 closed thirds and 2 open sixths so there can bo no draughts, (it is windy here). Also it has IR sensors, so stops if no-one wants to go through. Simple pleasures. Oh, and the breakfast is excellent!

Yes that's pretty, but surely we have introduced angles bigger than 90˚ by the time we want the addition formula, so what's with a proof that only works when 0<α<α+β<90˚? I move to defns based on the unit circle, and then a proof of cosine addition is simple, and the others follow.

What is the oldest consumable in your household? I bought this tub of grease about 59 years ago. I don't use it often but used a little yesterday morning. Should last a few more years.

Here it is

Good Q. I get this, may not be right: the x co-ord is half the angle of the slice. For x<π/2 it's 1+cos(x) with the rectangle oriented with one side across the mouth of the slice. For π/2<x<3π/4, width is 1. For x>3π/4 the orientation switches so that one side is one of the radii of the slice.

The greengrocer's apostrophe has a different meaning in Spanish.

In fact here it is

This is the simplest case. To show that if a body with a pivot is in equilibrium, the sum of the moments of the external forces is 0. I did it on the board with a lot more spoken words: I hope this is sufficient.

Bluesky now has over 10 million users, and I was #6,179,921! Turns out I'm a chameleon: