#MathMonday I love it when there are useful, “everyday”, applications of a mathematical theorem. Here’s one of my favorites: Take a level table wobbling on uneven ground. The Intermediate Value Theorem guarantees that rotating the table in a circle, less than a quarter turn (for a 4-legged table), will find a spot where the table sits perfectly without wobbling! No need to shove napkins under the “short” leg. (#Proof available upon request.) #calculus #IVT

Growing up I learned to count in base-11 from watching CBC 🇨🇦📺. We counted from 1 to 10A.

#MathMonday

Here is a #math question from a line of my #economics research:

There are functions which are discontinuous everywhere (Dirichlet function) and non-monotonic continuous but non-differentiable everywhere functions (Weierstrass function). Can a monotonic function be continuous but non-differentiable everywhere? Can the Lebesgue integral of a non-negative discontinuous everywhere function yield a continuous but non-differentiable everywhere function?

#MathMonday #realanalysis #measuretheory

#MathMonday What was it that made you want to be a mathematician? When did you fall in love with #math ?

For me it was Asimov on Numbers in the 7th grade and coming to understand that there were different magnitudes of infinity. I needed to be able to prove this. Hilbert’s Hotel and Cantor’s proof of the uncountability of the Reals set me down a path I’m still on.

https://en.m.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

https://en.m.wikipedia.org/wiki/Cantor's_diagonal_argument

#MathMonday #proof continued.

If the temperature at x=0 is the same as x=1 we’re done! If it is less than, then f(0)<0. Note f(1)=-f(0)>0. As long as temperature varies continuously, then there is an x* between 0 and 1 such that f(x*)=0 (Intermediate Value Theorem), so it has the same temperature as its opposite point.

If the temperature at 0 is greater than at 1, then f(0)>0>f(1) and the IVT still holds.

Note that this works for any closed shape drawn on the globe, not just great circles.

It’s #MathMonday.

Time for my favorite proofs,interesting problems, and open questions. Today a proof:

Draw a circle on the globe. There are two points directly opposite each other that are the same temperature!

#proof Pick a point on the circle, label it 0 and the point opposite 1. 0.5 is the point halfway clockwise between 0 and 1. 0.25 is one quarter from 0 to one, etc.

Create a function f(x) which is the temperature at x less the temperature opposite point x.

1/2

RT @Rainmaker1973@twitter.com

log(😅) =💧log(😄)

#MathMonday
#MotivationMonday

🐦🔗: https://twitter.com/Rainmaker1973/status/1566851027181228035