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#induction

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The 11yo is now regularly cooking their own pasta with the #induction hob, and wow is that a lot less for a parent to worry about than the hot electric stovetop or an open gas flame (it's still scalding hot water though, make sure they know how to manage it.) There is even a timer setting so it just turns off if you forget. Also, I highly recommend raising a self-feeding child 😌

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Akshar Varma

@BernhardWerner My favorite alternative #proof strategy for #induction proofs are #combinatorial (counting) proofs.

I suppose the standard example might be the proof of the coefficients in the binomial theorem expansion, or for the sum of binomial coefficients being powers of 2. These can be proved by induction, of course, but I'm not sure that's common given how easier it is to do a counting proof. It is also much clearer and avoids tedious algebra.

One I like is proving that the sum 1 + 2 + 3 + ⋯ + 𝑛 is 𝑛 + 1 choose 2, the binomial coefficient \(\binom{n+1}{2}\). Bijection proof, counts the same thing in two ways. The thing being counted is the number of ways of choosing two things (distinct, without repetition) from the set {0, 1, ..., 𝑛}. By definition, it is the binomial coefficient we want. The other way to count is to fix the larger number 𝑘, the remaining choices are any of the 𝑘 numbers from 0 to 𝑘 - 1. Thus, across all possible larger numbers, we get the sum from 1 to n.

An alternative alternate proof of the same, slightly more geometric is as follows: arrange dots in a triangle, 1 on row 1, 2 on row 2, and so on up to row n, with n dots. Add a phantom row of n+1 dots below. We want to add up all dots in first n rows: ∑ 𝑖. If you think of all of this as a binary tree/DAG, then every dot has two children (imagine Pascal's triangle). If you pick any two dots in the phantom row, their common ancestor is unique. So counting dots is same as picking two dots in phantom row. Which is the binomial coefficient we want.

Benjamin and Quinn's book on combinatorial proofs is amazing for interpretations of this form (I learned the first proof from it). See also: en.wikipedia.org/wiki/Combinat

en.wikipedia.orgCombinatorial proof - Wikipedia
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Susan Kaye Quinn 🌱(she/her)

I shot this video w/Penn Environment last fall and the crew did an amazing job putting these clean energy stories together.

*Especially* given the ongoing, escalating assault on the environment, I'm proud that the things I've already done (#solar #induction #EV #native #plants) will keep on making a difference for decades to come, regardless.

"they’re investing not only in cleaner energy for themselves, but also a cleaner world for their grandchildren’s generation."

environmentamerica.org/pennsyl

Stories from our Pittsburgh Solar Tour Meet PennEnvironment volunteers Dave Blair and Susan Quinn and Pastor Dave Carver who are all experiencing the benefits of going solar! environmentamerica.org
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CelloMom On Cars

Battery induction stove

"Because the new range has a battery, it’s possible to plug into an existing outlet.

The tech is designed to charge the #battery from the grid when the most renewable energy is available.

While some #induction stoves have an annoying buzz while they work, Charlie is silent. And if a storm temporarily takes out the grid, both the stovetop and oven can keep going, with enough stored power for three to five meals."

fastcompany.com/91158731/why-t

Fast Company · Why this new induction stove has a battery inside—and old-fashioned knobs instead of a touchscreenThe ‘Charlie’ range is designed to make it easier to switch from gas to electric.
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Sheril Kirshenbaum

The #food system is one of the most meaningful places to address #ClimateChange.

Have you been curious about switching from gas to #induction? This game-changing cooktop is faster, cleaner, more precise, and a win for the environment.

My new ep of Serving Up Science is all about why it makes sense to switch when it’s time to replace your range. youtu.be/JyTvHQnHq14?si=4twIzt #energy

YouTubeGas vs Induction Stoves: The Heated Debate | Serving Up ScienceBy PBS Food
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