Michael H 🏳️‍🌈

To all the people checking out my profile after a few mildly successful tweets: I generally only post replies about solutions to maths problems, there's nothing really to be found here

@OxUniMaths As the limerick goes: If M's a complete metric space And non-empty, we know it's the case That under the action Of any contraction A point must remain in its place

Mathematicians lend their names to theorems. But behind the name is a life. In Stefan Banach’s case a traumatic one as a Polish man living through World War II. Banach’s contraction mapping theorem features in our latest 1st year student lecture. Watch: youtube.com/watch?v=PEosQo…

@AlgebraFact Proof: the last (rth) element is either not in the chosen selection, so there are (r-1)Ck ways to choose the k elements, or it is, so we need to choose only k-1 from the other r-1 These selections are disjoint, so we can add them.

For integer k:

@Cshearer41 If not a hidden circle, then it must be congruent triangles 😊 (I bet there's a circle I missed though...)

The three smaller squares are the same size. What’s the angle?

@Cshearer41 Using, of course, a hidden circle

Four squares. What’s the green area?

What is the best an actor has ever looked on screen?

@RogerBlack3 @RevRichardColes It was destroyed in a fire in WWII en.wikipedia.org/wiki/Saint_Mat…

@RevRichardColes The angel in the first appears to have a belly button - some mistake, surely. By the way, if it's lost, how come there's a photo of it?

@Cshearer41 I had to triple-check the solution to those simultaneous equations at the end

The centre of the semicircle lies on the perimeter of the quarter circle. What’s the shaded area?

@Cshearer41 Assuming it is a quarter-circle in the diagram:

The green triangles are congruent. What’s the angle?

@Cshearer41 It turns out I can't draw an arc to save my life

The area of the red square is 12. What’s the total yellow area?

I guess I'm now an x-user?

@HerefordCS @HCSHead Nice! This method is called 'divide and slide', and I think it's commonly taught in other countries but not here (as it disguises what's really going on). Always great to see some initiative from students!

A Hereford Cathedral School Year 10 pupil has wowed the School's Maths Dept staff by devising an alternative method for solving quadratic equations. herefordcs.com/.../year-10-pu…... #mathshack #GCSEmathshack #quadraticequations #quadraticequationshack #GCSEmaths @HCSHead

@BBCWorld I'm not sure I fully trust any corn-related analysis that doesn't come from @SwiftOnSecurity

The US is the world's biggest corn exporter - but for how long? bbc.in/44vJ60Q

I reached my tweet viewing limit in the app before 9am, but I can still read them OK in the mobile browser... #RateLimitExceeded

Times are so hard we're going to the Off Peak District for our family holiday this year.

@Cshearer41 I don't think I've thought of shearing the *unshaded* sections before 😀

What fraction of the total area is shaded?

@SoVeryBritish On the way back from each holiday we'd compile a list of memories of the trip, and it would be full of stuff like "when we drove the remote controlled car into a tree"

Shoutout to everyone who goes on holiday, sees all the main sights and famous landmarks, yet ends up with their favourite bit being a random moment in a nondescript place. “The best part? No, not the cathedral. Probably the sandwich we had in that petrol station when it rained”

@FergusPowell I would absolutely love to have something that uses number 5

11 is my fave

@alistaircoleman I'm so sorry to hear of your loss

My father, Professor Jonathan Coleman, died peacefully at home this afternoon. I’ve never been entirely sure how old he was, but I think he was 86. Or 85. He’d been living with dementia for years, and was patiently cared for by my stepmother. I feel strangely calm about it.

I was at a sensational combinatorics seminar in Cambridge yesterday, reminiscent of the time I had been tipped off that Andrew Wiles's seminar at the Newton Institute on Wednesday 23rd June 1993 might be worth going to. 🧵 arxiv.org/abs/2303.09521