Benjamin Cornish

@mathematicians-pod.bsky.social

Teacher. Mathematician. Podcaster https://ko-fi.com/benjamincornish

I've been struggling to make a joke about how "a man with a hammer sees only nails." Except I have a rusted wheel bearing that I need to hammer "out", whilst a happer typically pushes "in". I was delighted to discover a "slide hammer" Is a real tool. And now I own one. P.s. got the bugger

BildBild

Try this. Take a number, n, split it into proper prime divisors. Write those, ascending, as the place values for a new term base n. Repeat this recursively. I think only 3 non-prime-powers will terminate. 10-> 25_10 25-> 5_25 5->0 12-> 23_12 27-> 3_27 3-> 0. What is the third number?

Here is a full set of iceberg diagrams. The score is how many full squares there are, counting the ones above the waterline as positive and the ones below the waterline as negative. Given a list of integers (eg 8, 6, 0, -5, -8) can you make an iceberg that will produce exactly that list? #MathSky

The whole image has a square grid marked in faint blue lines.
At the top, a heading in blue reads "Iceberg diagrams".
At the bottom, there is a horizontal blue line, with the space below it shaded in blue.
Five identical grey shapes with black edges sit at different heights relative to the blue line. The edges are made by joining gridpoints horizontally, vertically or diagonally.
Starting at the top left, the edge goes one step right, one step diagonally right and down, two steps down, one step left, one step diagonally left and down, one step diagonally left and up, one step up, one step diagonally right and up, and one step up, to come back to the start.
The leftmost shape is fully above the blue line and has the number 8 written above it.
The next shape is one gridline lower and has the number 6 written above it.
The next shape is one gridline lower and has the number 0 written above it.
The next shape is one gridline lower and has the number -5 written above it.
The next shape is one gridline lower and is now fully below the blue line, and has the number -8 written above it.