A network diagram showing the orbits of numbers with starting values between 1-250, and path lengths of at least 10. Six cycles have been identified, and coloured.

My first attempt at a #DiscreteDynamicalSystem

Take a number, n
If (n-1) is prime then map n -> n^2
If (n-1) is composite then map n-> Aliquot sum of (n-1)
Numbers 1-19 all end in a cycle. I am not sure about 20.

eg. 6 -> 36 -> 13 -> 16 -> 9 -> 7 -> 6.

#mathsky
#recreationalmaths
#mathsart

A393283 - OEIS

New oeis.org/A393283 just dropped.

Take a triangular array starting (0),(1,0) Now draw a ray from the tip down to the next term. Each new term is the sum of terms on or adjacent to this ray.

0
1,0
1,1,0
2,3,2,0

Try this in mod 2 for a #cellularautomata.

#mathsky
#sequences
#recreationalmaths

Euclidea - Geometric Constructions Game with Straightedge and Compass

Today, in honour of #euclid, I sit down with the creator of www.euclidea.xyz . Easily my favourite #recreationalmaths game

Play the game, love the game, hate the game then wonder how it was made. After that emotional rollercoaster, join me on my podcast to listen to the creator share all.

#mathsky

The Secret World of Flexagons - Scott Sherman, Yossi Elran and Ann Schwartz *** A great book for the right audience. When I was a teenager I loved Martin Gardner's Mathematical Puzzles and Diversions books. They combine...

Review: The Secret World of Flexagons: Scott Sherman et al *** - If this paper-folding and flexing branch of popular maths is your thing (or it brings back memories of Martin Gardner), this is an absolute must-have book. popsciencebooks.blogspot.com/2025/04/the-... #bookreview #recreationalmaths

Euclidea - Geometric Constructions Game with Straightedge and Compass

Very excited for my interview with the creator of www.euclidea.xyz tomorrow.

Easily the best #euclideanconstruction game available.

Check "The Mathematicians Podcast" in a few weeks time to hear what he has to say about the gamification of ancient Geometry.

#recreationalmaths #mathematicianspod

6 panels showing the construction of the intentre of a triangle using circular arcs each centred at the intersection of the perpendicular bisector and the opposing angle bisector.

Today I was messing around on #goegebra just doing some #recreationalmaths, and I found an invariance that was new to me.
The 'centre' of a triangle can be defined in thousands of different ways, but often the definition has multiple constructions.
Enjoy my construction of the #Incentre

#mathschat

Fun fact.

If you inscribe in the same circle a pentagon, hexagon and decagon then their side lengths could form a right triangle.

Is that true for any other n-gons?

#mathsky #recreationalmaths

A geogebra construction of 5 mechanical linkages which trace out a few concentric hearts in shades of pink and red.

www.geogebra.org/m/v6decvme

MFW people ask me if I enjoy #geogebra

Another #link-abet character, expanding into emoji.

Have a go yourself with the interactive geogebra website.

#recreationalmaths #mathsky #mathartmarch

Link-abet 'x' Link-abet

Today my proudest achievement will be my #link-abet letter formally known as twitter.

Join the game on #geogebra

Create a letter of the alphabet using mechanical linkages.

www.geogebra.org/m/hcmmndrq

#mathsky #recreationalmaths #mathsfun

#link-abet.

Can you create a set of mechanical linkages to write a letter of the alphabet.

Rules: must be driven by A=(0,t) with 0<t<1

I think this is the best letter 'e' I can do after an evening of playing around. See if you can do better!

#recreationalmaths #mathsky #mathsgames

Link-abet 'a' Link-abet, letter a

Big announcement:

I'm creating a new game, called #link-abet.

Can you create a set of mechanical linkages to write a letter of the alphabet.

Rules: must be driven by A=(0,t) with 0<t<1

I will go first:
www.geogebra.org/m/mawgx5hr

#recreationalmaths #mathsky #mathsgames

Arrange 9 consecutive numbers into the 3 by 3 grid, so that… (a) the product of the 3 numbers in each row are 16588, 16200 and 13524 (b) the product of the 3 numbers in each column are 16146, 14784 and 15225 (c) the sum of the numbers in the 2 by 2 grid shaded grey in the top left corner of the 3 by 3 grid is 99.

Today's #OCRMathsPuzzle is inspired by some great 'yohaku' puzzles that we've seen on here recently @mikejacobs.bsky.social

Arrange 9 consecutive numbers into the grid, to meet the requirements below!

Have a great weekend! 😀
#UKMathsChat #arithmetic #RecreationalMaths

The Mathematicians Podcast | Ben Cornish Where we explore the historical figures that count. An in-depth look at the history of mathematics, in chronological order, looking at the people, the theories, the ideas - with as fewer gaps as possi...

Competition time:

What's the largest number you can write that has no repeated consecutive substrings of digits?

Eg. 987978 good. 987987 bad, (987-987)

#mathsky #recreationalmaths #algorithms

(Spoiler alert for an upcoming episode of mathematicians.podbean.com)

Euclidea - Geometric Constructions Game with Straightedge and Compass Euclidea is all about building geometric constructions using straightedge and compass. About doing it the fun way. With Euclidea you don’t need to think about cleanness or accuracy of your drawing — Euclidea will do it for you. But it’s also a game. A game that values simplicity and mathematical beauty. Find the most elegant solution — the one, which is built in the least possible moves, — and you’ll get the highest score.

Just finished writing my interview questions for an episode on Euclidea the game, with an expert guest: the game's creator.

If you've not yet tried it. You're missing out: www.euclidea.xyz/en/

#talkmaths #recreationalmaths #geometry

The image shows the diagram associated with the puzzle: A kite is drawn within a circle. The vertices of the kite just touch the circumference of the circle. The base angle of the kite is 60°.

This week's #OCRMathspuzzle is here!

A kite is drawn within a circle, as seen below.
The vertices of the kite just touch the circumference of the circle.
The base angle of the kite is 60°.
What is the exact fraction of the circle that is covered by the kite?

#maths #UKMathsChat #RecreationalMaths

2025 is the product of a prime number, a square number and a cube number. 2025 = 3 x 25 x 27 What is the next year that will also be the product of a prime number, a square number and a cube number?

2025 is a square number,
but did you also spot that 2025 is the product of a prime number, a square number & a cube number.
2025 = 3 × 25 × 27

What is the next year that will also be the product of a prime number, a square number and a cube number?

#OCRMathsPuzzle #UKMathsChat #RecreationalMaths

Nice, that makes at least two solutions. My solution had each edge adding to 33.

What's the greatest and least edge totals?

#RecreationalMaths #OCRMathsPuzzle