Benjamin Cornish

@mathematicians-pod.bsky.social

125 Followers 89 Following

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

A children's wooden train set. Designed with pleasing loops.
Source: https://i.sstatic.net/6w4OZ.jpg A diagram showing the possible distinct arrangements of 4 lines, grouped by number of intersections.
An extract from a statistics exam - this one on combinatorics
A screenshot of a podcast analytics page showing the number of listeners from various countries. Including one with the label "Palestinian Territory, Disputed"
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.
3*3 bingo card of phrases I say a lot each day, eg "have you checked the formula book?"
Geogebra plot of P_5(t) with coefficients as 2D vectors, the drawing is almost like a signature.
Geogebra plot of a quartic equation in t, with coefficients as 3D vectors
Little Miss Cornish's hair this morning.
A fractal tiling of a Christmas card (With a snowflake, Koch snowflake and spiral of tinsel on a cone: Text reading "Merry Christmas TMIP"). The tiling is composed of 78732 individually coloured pentominoes, arranged in batches of 9 to form a larger pentomino, which are in turn arranged in batches of 9, etc etc up to a larger grid of 6*10, 12 top layer pentominoes
A headshot of me with a pentomino tiling mosaic - this version shows the original 6x12 grid, and each layer of recursive tiling.
A headshot of me created by 8748 individually filled pentominoes, tessellating a rectangle in a near-random arrangement.
Shaun the sheep, birds eye shot of a goat eating grass in a spiral
Screenshot of a Wikipedia article for "The three gods riddle"
A Reddit screenshot: This sounds like a job for a fermi approximation. I buy a week's food for 2 people when I shop. I think I visit less than 1 in 1000 items. In that for every 1000 distinct products they sell, I think I have 1 of them. I think whenever I buy an item there are about 10 on the shelf, and probably another 10 behind the scenes. So 2x1000x10x2 = 40,000 weeks for 1 person. The average human lasts 4000 weeks. So 1 shop can support 10 people their whole lives. Edit. Formatting
A page of mindless doodles of polygon arrangements
OEIS entry. https://oeis.org/A011545
A marble run set up, from the Gravitrax brand.
Figure 1. The 30-gon with its diagonals. There are 16801 in- terior intersection points: 13800 two line intersections, 2250 three line intersections, 420 four line intersections, 180 five line intersec- tions, 120 six line intersections, 30 seven line intersections, and 1 fifteen line intersection.
The Insatiableness of Avarice. Though the covetous grown wealthy See his piles of gold rise high; Though he gather store of treasure That can never satisfy; Though with pearls his gorget blazes, Rarest that the ocean yields; Though a hundred head of oxen Travail in his ample fields; Ne'er shall carking care forsake him While he draws this vital breath, And his riches go not with him, When his eyes are closed in death. -Boethius, 524 CE
Origami boat made from green and yellow A4 sheets
A square based stepped pyramid consisting of 8 layers of Duplo
Full text here: https://crossworks.holycross.edu/hc_books/63/
Red-green alternating pattern of Duplo. Apologies for RG colourblind choice
A beautifully crafted castle made from duplo
Brio train track arranged into a unsettling spiral
A picture of my camp stove this morning
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.
Screenshot of calculator.net showing 2 dice concatenated to read 41, which is prime
A screenshot of Newton's Principia, Book 1 Section 5 Lemma 17, which discusses conics.
A child's rainbow toy, but stacked in reverse order into a spiral Photo my own