I watched a YouTube video which said Rachmaninov wrote 7.5 x 10¹⁸ notes during his lifetime as a composer. Could this be true?

See:

https://learn1.open.ac.uk/mod/oublog/viewpost.php?post=260010

I found this in a puzzle book and thought it would be not too hard, but it was more tricky than I expected. Making sure you haven't missed any triangles, or double counted any, is quite slippery.

Here are the possible kinds of triangle:

Each of these can occur in five positions, so I thought at first the answer is 6 x 5 = 30, but I was mistaken, because config. e has chirality, i.e. handedness; the triangles can be aligned right or left, and so we get a total of 35.

After more investigation I found a fairly recent paper which gives a general formula for a regular polygon with any numbers of sides, but for larger numbers it gets quite complicated. 

I liked this problem, for the original pentagonal case, because it is easy to grasp, less simple than appears at first but is still solvable with some careful working.

I'll post a link to the paper about the general case for anyone interested.  

Opening the mouthwash 

Was like a tiny obstacle course.

Designers, are you listening?

How many triangles can you find in this diagram? I don't just mean ones whose vertices liu on the outer pentagon, I mean all the triangles visble.

 With apologies to Raymond Smullyan.

Nobody told me

The warp drive was not reversible

Now I’m kinda stuck.

Old English for oak was ek, I think (German is Eiche) but that has mutated into oak in Modern English. The “corn” bit presumably means seed, and so why don’t we call it an Oakcorn?

Try saying it at normal voice level, Oakcorn. 

Try whispering it. Is that different?

Why?

This striking moth has a wide range outside Britain, but historically it was rare here and only found in the Channel Isles (thus the name) and one location in Devon.

However like many species it has been expanding its territory and has now spread north as far as Cambridgeshire, where it popped up in my garden.

This picture of the resting insect doesn't begin to show how spectacular it is in flight; sadly it didn't stay around long enough for us to video it.

I love squirrels, seeing them often in my garden, and was fascinated to hear recently that their brains may grow in autumn and shrink again in spring. 

The reason for this might be that the task of storing a winter food supply in a way that's easy to find again takes a lot of mental effort, to organise and memorise the cache locations.

Other mammals adapt for winter in significant ways; stoats and mountain hare change the colour of their coats; hedgehogs and bears hibernate. There is also evidence that shrews shrink both body and brain, to survive with shrunken resources.

So the idea about squirrels is plausible, and it's supported by research findings, but of course it's hard to be sure and there is still debate.

There's a good article here about a leading researcher and her liking and fascination with these clever little beasts.

Studies of squirrel brain regeneration may reveal clues about how to slow Alzheimer's disease, because in at least one form, the cells squirrels seem to regenerate are the ones that sufferers appear to be losing? Could mental activity, such as doing puzzles, help? It's often been suggested and there is some evidence in favour, I recall. It's an alluring possibility but no more at this stage.