Benjamin Cornish

Just had a fun conversation about Primitive Pythagorean Triples with Carol Jacoby from: theartofmathematicspodcast.com

Can you find a coordinate M:(a,b) such that |OM|=|MA|=k, with O:(0,0) & A:(20,20) and k an integer?

You should be able to listen in at the end of March

#talkingmaths
#mathsky

Happy half term holidays!

I am celebrating by releasing another episode of #TheMathematicianspod. Find out about Systems A & B today with a double bill of 'Babylonian' Mathematicians.

www.podbean.com/eas/pb-vjqv3...

#talkingmaths
#mathsky
#mathspodcast

Again in mod 2, a companion sequence

oeis.org/A392906

[0]
[1, 0]
[1, 1, 0]
[0, 1, 0, 0]
[0, 0, 1, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 1, 0, 0]
[0, 0, 0, 1, 1, 0, 0, 0]
[0, 0, 1, 0, 0, 1, 1, 0, 0]
[0, 0, 0, 0, 1, 0, 1, 0, 0, 0]
[0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]

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

I just lost a game of rock paper scissors, four - nill, to a lobster

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.

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

Looking forward to watching. I managed to make my masters thesis rely on the HBT. Was it necessary? Probably not. Was it sufficient to delight me? Yes

My latest obsession with maths teacher bingo has now grown to a 5*6 grid... I might have to stop here.

#alevelmaths

New #mathspodcast episode just dropped of the #themathematicianspod, if you want to listen to #Baudhayana again, but with slightly updated mathematics, you will love the episode on #Apastamba

A tower is built with one brick on top of another. Come meet India's second brick!

#talkingmaths
#mathsky

Nine 'rules' of ratio tables laid out in a 3 by 3 grid format.

Some 'aspects/rules' of ratio tables ... collected together as an aid to proportional reasoning.
'El. V–16' = Euclid's Elements Book 5 Proposition 16

#UKMathsChat
#iTeachMath

a(5) = 7 since the iteration gives [2, 2, 4, 3, 2, 1, 2, 2], with 7 terms before the pair 2,2 repeats.

New sequence just dropped to the #oeis

Start with the numbers [2,2,...] Then each new number is the product of the last two, written in mod n. The sequence stops when there is a repeating pair of consecutive numbers.

a(n) is the length of the above sequence.

oeis.org/A389543

#mathsky

Who wants to play: "Guess what I've been teaching"

#alevelmaths

Day 2 is ready

Oh I wrote that on the board just to check you were paying attention. *Ahem*

(In my class we are all allowed to make mistakes... "But these were just the mistakes I made that you noticed, I wonder how many you missed")

A cross-section of the celestial sphere annotated with transliterated Sanskrit terminology.

A diagram for a diagram-less tradition; gradually making some sense of Brahmagupta's Khandakhadyaka. With a couple of shadow measurements and the angle of the rising sun he could calculate the time of day. Astonishing really.

3*3 bingo card of phrases I say a lot each day, eg "have you checked the formula book?"

I've started a "Maths lesson Bingo" with my students. Can anyone suggest some phrases for my next card to be 4*4?

#alevelmaths

That's not a position vector, it's just 3 components wearing a trench coat.

Vector-bet Vector-bet Game

New game just dropped: #Vector-bet

Can you create a letter of the alphabet using a polynomial with vector coefficients?

Have a play for yourself with my #GeoGebra widget:
www.geogebra.org/m/hv99xfkj

Featuring drag and drop vector tools and a squiggly pen!

#sillymaths
#mathsky

Geogebra plot of P_5(t) with coefficients as 2D vectors, the drawing is almost like a signature.

Follow up from my #alevelmaths student:

If you use 2D vectors for a high order polynomial, the resulting plot is, once again, 2D - however it is highly disorganised: Here we see a Quintic Equation.

#mathsky

Geogebra plot of a quartic equation in t, with coefficients as 3D vectors

A great observation from my #Alevelmaths student: If you create a polynomial with vector coefficients $r=a+bt+ct^2+dt^3...$ you can get higher dimensional equivalents of the polynomial. Here is a 3D quartic equation.

#mathsky

New sequence just dropped to the #OEIS
Have you ever wondered how many sides are needed on a k-gon such that an inscribed and circumscribed k-gon calculates the area of a unit circle with accuracy bounds up to n digits? I know I have!
If you have a 12-gon will tell you π=3
oeis.org/A391013
#mathsky

🎶There in the middle, three medians meet now
Balance is found where they all intertwine
Share every side in a fair little split, how
Mass would be happy—this center’s just fine

My new #OEIS sequence just dropped.

Least k > a(n-1) such that k + the sum of all previous terms = 0 (mod (k-2)), with a(1)=1 and a(2)=2.

1,2,3,4,...

(1+2+3+4+n) Is a multiple of (n-2).

...5,...

What comes next?

oeis.org/A390783

#mathsky

Little Miss Cornish's hair this morning.

Very happy with this two cord braid this morning

I might say one feels more "emotionally accurate"

Similarly I use ‽ When I am coding a rhetorical if statement

I am delighted to share with you my first episode of the new year, and my first for the history of maths in #India.

Come and listen to some instructions with rope with #Baudhayana.

www.podbean.com/eas/pb-tueww...

#mathstalk
#mathsky

Hey folks, I'm looking to record another episode of #Un-NaturalNumbers, the YouTube maths chat show, soon. If you want to have a go at presenting a cool fact about the number 8 give me a buzz.

Or pass the invite on to someone

All you need is good WiFi and something interesting to say

#mathatalk

Write down the Fibonacci numbers, next find the remainder of each one when you divide it by your favourite number. Then notice how long it takes for a repeating cycle.

Rinse and repeat.

#mathsky
#pisano

I am inclined to agree...