Wayne Burrows

@jamestanton Generally, we can fit a quadratic with rational coefficients.

There is no polynomial with integer coefficients along with three distinct integers a, b, c such that P(a) = b, P(b) = c, and P(c) = a. What about a polynomial P with real coefficients? Might one be able to find three real numbers a,b,c so that P(a) = b, P(b) = c, and P(c) = a.

@jamestanton Same three points with three of the coefficients not rational.

@jamestanton P(0)=1 P(1)=2 P(2)=0

@jamestanton We need (a-b)|(b-c), (b-c)|(c-a), and (a-c)|(b-a) which is not possible. a<b<c WLOG |a-c|>|b-a| so (a-c) does not divide into (b-a).

The polynomial P(x) = a + b - x has P(a) =b and P(b) = a. Find a polynomial with integer coefficients along with three distinct integers a, b, c such that P(a) = b, P(b) = c, and P(c) = a.

A polynomial P with integer coefficients has P(a) = 3, P(b)=2, and P(c) = 1 for three integer inputs a, b, and c. Explain why a, b, and c must be consecutive integers.

@DavidDack 2-2:20 walking. Think I could have gone sub 2 but I never did another one. Did 19 km a month or so later in 1:50

Where does your half marathon time rank? 2:20+: survived it 2:00–2:20: solid 1:45–2:00: strong 1:30–1:45: fast sub-1:30: very fast sub-1:20: nasty work What’s yours?

@DavidDack I think of 25 as average as I used to do light runs out of the house at 5min/km. Now I am older I dream of running 5min/km but my Garmin is working on it for me.

What counts as a “good” 5K for a recreational runner? Sub-35? Sub-30? Sub-25? Or depends who’s asking? Be honest. Everyone has a secret line.

@ewjonker @ZahlenRMD a_1=1 a_2=a_1+1=2 a_3=a_2+2=4 ... These are one more than the triangular numbers (offset by one position). A_100=T_99+1=4951

@ZahlenRMD a₁=1 a₂=a₁+2=1+2 a₃=a₂+3=1+2+3 aₙ=∑ᵢ₌₁ⁿ i=(n+1)n/2=½n²+½n a₁₀₀=½×100²+½×100=5050

Recurrence relation #sharingisthenewlearning

@jamestanton Nice. I like ugly algebra :) The recurrence relation looked like something that could be proved by induction so I had a go. I once showed a professor a couple of pages of algebra. He said "yuck" but I would give you credit for it. Then showed me another way.

@WayneJBurrows Or ... maybe you can avoid algebra! For a derangement of {1,2,3, ...,N} there are (N-1) options as to where 1 can go, say to position k. In each of those instances, split into two case: k goes to 1, and k does not go to 1.

A sequence satisfies the recursive relation shown. What is this sequence if A(1) =1, A(2) = 2? What is this sequence if instead A(1) =0, A(2) = 1?

@awkwardgoogle i hope the driver acknowledged the truck driver.

The man thought he was being cut off…seconds later, he realised the truck driver had just saved his life!!

@TheZeitgeistNZ This is political partisan dogma not a Human Rights Issue. We have an equal pay act. It ensures equal pay. If it is not being adhered to take action under that act don't grandstand on the world stage.

A complaint is being taken to the UN by the Council of Trade Unions and the NZ Human Rights Commission over the government’s changes to pay equity laws - the complainants argue NZ is no longer fulfilling its international obligations to provide women with equitable pay and is engaging in systemic discrimination. 1News article - 1news.co.nz/2026/05/06/com…

@FullTwatforward Sounds like she is sexist.

Golly... I wonder who she has in mind?? Is this her independent opinion?? 🙄🙄 "Former NZ PM Helen Clark says a female UN Secretary General would be 'transformative'" abc.net.au/pacific/progra…

@MrBeast I felt sure I would be the one.

If this tweet has exactly 1 like in 24 hours I’ll give that person $1,000,000

@jamestanton 0 . 1 5 0 8 9 1 6 3 2 3 7 3 1 1 3 8 5 4 5 9 5 3 3 6 0 7 6 8 1 7 5 5 8 2 9 9 0 3 9 7 8 0 5 2 1 2 6 2 0 0 2 7 4 3 4 8 4 2 2 4 9 6 5 7 0 6 4 4 7 1 8 7 9 2 8 6 6 9 4 1 0... These 81 digits repeat.

@jamestanton 110/729 has a recurring decimal representation.

In a base-ten place-value chart, ten dots in any one box "carry" to become one dot, one place to the left. (E.g. 0.0|0|13| = 0.0|1|3). Place dots in all the boxes: N^2 dots in the Nth decimal place. Prove that after all the carries, a repeating pattern will appear!

@zoekennedy @OhhHeyAlana @KeruboSk @MomoStJohn If you are denying that relationship break ups cause harm then I don't think you understand the world.

@OhhHeyAlana @WayneJBurrows @KeruboSk @MomoStJohn Quite and also ‘relationship break ups cause harm’. We all know that’s suggesting that the person breaking up was injuring the person who attacked their car.

Nothing makes you a feminist more than having daughters. My oldest had been dating a boy from church for a while and for her own reasons, she ended it on Sunday. Monday morning, she walked out to find her car covered in syrup, shaving cream, and dish soap. Our exterior cameras clearly show the boy and a friend doing it overnight. Local police are dragging their feet, calling it a “prank” and suggesting I “calm down and think about the boy’s future” since he is leaving for the Army this summer. I was left standing there with a 17 year old who is hurt, confused, and trying to figure out why this is being treated like nothing, and she was told to worry about his future instead of justice. I am starting to understand how often the person who was wronged is asked to carry the weight so things stay easier for the person who did it. I do not know how women live with that, being expected to absorb it, excuse it, and move on while the people who hurt them are protected from the consequences. ~ abnerdark182 ( threads)

@Sekhmet_Eins @KeruboSk @MomoStJohn More reading comprehension problems. No excuse.

@WayneJBurrows @KeruboSk @MomoStJohn And this is your excuse for the boy damaging the car?

@zoekennedy @KeruboSk @MomoStJohn Do you have a reading comprehension problem? "Violence even to property is never justified." No justification for me. I am just saying we might not know the full story. That does not justify violence.

@WayneJBurrows @KeruboSk @MomoStJohn Why are you trying to justify terrible behaviour

@mauriceraiti What is the evidence of that? Why the silence from almost every official quarter including from Maiki Sherman herself. So far it seems credible that Maiki called Lloyd a faggot. Against that there has only been innuendo denied about what Lloyd might have said to Maiki.

This media attack on Maiki Sherman shows how biased our media is when they would have known that Lloyd Burr made a racist slur to Maiki but didn’t report it. Maybe she should have held back but fuck that.