Benjamin Cornish

I was playing crazy golf with a bunch of topologists, but they kept arguing over the definition of a hole-in-one.

Are there any invariants, or is every (square-)orientation possible ?

I really like this. She's in bed now, but next time. I'm a big fan of the measuring idea. We did do 'putting towers in order of size', and which towers have more blocks

Red-green alternating pattern of Duplo. Apologies for RG colourblind choice

If I say:
Any square (4*4 or 8*8) may be rotated by 90 degrees, if the pieces are fully enclosed in the square.

Is it possible to sort all the greens to the left and reds to the right?

#playmaths
#mathschat
#mathsky

A beautifully crafted castle made from duplo

Here is my Duplo castle. Can anyone suggest some Duplo based maths that I can use to enhance my daughters play time?

#playmaths
#mathschat

Brio train track arranged into a unsettling spiral

Spoiler for my next YouTube video. Can you guess what it's about?

#mathsky
#briotrains
#railwaymazes

Getting ready to interview Dr Daffern on the intersectionality of ancient maths and ancient religion for #TheMathematiciansPodcast. Very much looking forward to episode 33, check it out in 2 weeks.

#mathstalk

Hey who invented #Trigonometry anyway?

Good question, come find out on this week's episode of #TheMathematiciansPodcast.

Wouldn't it be cool if he was the same guy who first identified a supernova, well if you insist

#mathstalk
#mathschat
#mathshistory

mathematicians.podbean.com/e/episode-31...

Open invite to Un-Natural Numbers Let us know if you want to be on a future episode. This form is mainly to get you linked in to the community. I will email you with a big old spreadsheet where you can see the recording dates and book...

Would anyone like to join me on the 6th of August to do episode 5 of #Un-NaturalNumbers the #MathsChat show all about the number 5. Would you enjoy sharing your favourite facts about 5 + An evening of delightful conversation with fellow maths enthusiasts

#mathstalk

forms.gle/nbVi7dezTNUp...

YouTube video by Un-Natural Numbers Un-Natural Numbers: Episode 3

Episode 3 has just dropped of #Un-NatrualNumbers, with excellent contributions from @hopeiona.bsky.social and @christianp.mathstodon.xyz.ap.brid.gy

If you are looking for a #MathsChatShow then check this out:

youtu.be/hZ9l5fF2x4w

#mathstalk
#mathsky
#KnotTheory
#SetTheory
#PalendromicNumbers

My first double bill of Mathematicians. Genius but not so prolific, and not to be ignored

Would you like to know who wrote book 14 of #Euclid's Elements? Did you want to see #integralcalculus before Newton? Then tune in

#mathstalk
#mathsky
#podcast

mathematicians.podbean.com/e/episode-30...

Very excited to record episode 4 of #Un-NaturalNumbers tonight with the fabulous @steckl.es and @paddymaths.bsky.social.

Tune in soon to YouTube for some fun facts about the number 4.

Or get in touch if you want to be a guest on a future show, open invite to all.

#mathstalk
#mathsky

My follow up question was going to be "...and how do I share the information on gas volume with the rest of the campsite in the quickest time?"

A picture of my camp stove this morning

So I am camping with a second hand gas canister. I have not been told how full it is, or how many hours of cooking it should last.

I can hear a 'slosh' when I shake it.

What mathematical steps would you take to estimate how many kettles I can boil?

#talkmaths
#mathsky

Moving up one dimension into Apollonian sphere-packing using POPs. I put together an implementation based on Kean Walmsley’s code, which itself is built on Ron Peikert’s original work from his paper “The Fractal Dimension of the Apollonian Sphere Packing.”

#creativecoding #generative #generativeart

YouTube video by Un-Applied Maths The biggest lies your physics teacher told you about pendula

My latest #MathsYouTube video is up. In this one I look at the 'Lies' of modelling in relation to pendula, and explore things like the small angle approximation, or the 'flat earth' of gravity.

Which model is better: pure or useful, you decide!

#alevelphysics
#mathstalk

youtu.be/8URfRjeuHA0

No, but in base three, the number 133 becomes 11221, where 1+1+2+2+1 = 7 (this step is always measured in unary) and 133=7*19. So the initial number 133 is a value, base independent, but the Harshad property holds in base 10, 3, and 8 (as well as some big ones, like base 127 where it is 16)

I'm intrigued, what do you mean?

Which also works on base 3 and base 8

Again both good ones. I have also set myself a goal of a multiple of 3/9, because they both work with the divisibility rules that are more widely known.

133 is a bit more spicy...

It does, but I was looking for one with no zeros.

Harshad Number A positive integer which is divisible by the sum of its digits, also called a Niven number (Kennedy et al. 1980) or a multidigital number (Kaprekar 1955). The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, ... (OEIS A005349). Grundman (1994) proved that there is no sequence of more than 20 consecutive Harshad numbers, and found the smallest sequence of 20 consecutive Harshad numbers, each member of which has 44363342786 digits. Grundman (1994) defined an n-Harshad (or n-Niven) number to be a positive integer which is divisible by the sum of its digits in base n>=2. Cai (1996) showed that for n=2 or 3, there exists an infinite family of sequences of consecutive n-Harshad numbers of length 2n. Define an all-Harshad (or all-Niven) number as a positive integer which is divisible by the sum of its digits in all bases n>=2. Then only 1, 2, 4, and 6 are all-Harshad numbers.

Potential fact for episode 4 of #Un-NaturalNumbers .

I spent most of my final minutes before falling asleep last night trying to think of a 3 digit Harshad number.

This gives a deeper insight into the rule of divisibility by 3.

#mathstalk
#mathsky

A Pappus Chain. An Arbelos-related chain of tangent circles between two tangent circles created with an inversion of a chain of circles between two parallel lines.

Hey, I just dropped my 27th episode on the history of Mathematicians in chronological order. Check out Apollonius, on conics. One of the whales of ancient greek maths.

#mathstalk
#mathsky
#themathematicianspodcast

www.podbean.com/ew/pb-j9r4c-...

Holy smokes Batman.

And this just happened to be published in the month that I needed it.

This is very nice

webhomes.maths.ed.ac.uk/~v1ranick/pa...

Knot theory and it's applications
Kunia Murasugi

I hope you'll check out the chat show when we air the episode next Wednesday

Just brushing up on my knot theory ahead of #Un-NaturalNumbers the maths chat show all about numbers.

Tomorrow we record episode 3, on the number 3. And I am planning to talk on knot theory.

See if you can find the significance, and whilst you wait have a go at this

#mathstalk
#mathsky

Screenshot of calculator.net showing 2 dice concatenated to read 41, which is prime

My #probability #starter for today's lesson:

If I roll 2 dice numbered (0,n) and place them next to each other, we can check if they are prime. But for what value 0<n<10 is the probability of a prime greatest?

#alevelmaths
#mathsky

A screenshot of Newton's Principia, Book 1 Section 5 Lemma 17, which discusses conics.

I just downloaded my own pdf of The Principia, this has given me a curious feeling, like reading a religious text. Below is B 1, S 5, L 17: where I will be making the case that Newton is citing Apollonius for his work on Conics.

Free copy: web.math.princeton.edu/~eprywes/F22...

#mathsky
#mathstalk