Brad Findell

Mathematics teacher educator, husband, dad, data junkie.

[Brad Findell @BradFindell]

@RanthonyClark Semper ubi sub ubi: Always where under where.

Oops. Wrong thread.

Seriously, here is pretty good list: https://t.co/TbRZbirR86

[Brad Findell @BradFindell]

@Mathowitz Thank you! When talking about reflex angles, we need this word! And I have (wrongly) told my students that we don't have a such a word.

Here is another useful word about angles: goniometer.

[Brad Findell @BradFindell]

@CmonMattTHINK A big part of the problem is that two-column proofs don't seem like explanations. Compare these four proofs.

[Brad Findell @BradFindell]

@robertkaplinsky But the sphere is not Euclidean!

[Brad Findell @BradFindell]

@Hillsdale This survey is partisan tripe not worthy of an institution that calls itself a college. Do better. Be better.

[Brad Findell @BradFindell]

@pickover

[Brad Findell @BradFindell]

@bowenkerins (A) Kidding.

(B) Sort of kidding.

(C) A more pedantic version of your best suggestion, "What number makes each equation true?"

[Brad Findell @BradFindell]

@VivekGRamaswamy You have misquoted. He said “the greatest *terrorist* threat to our homeland is white supremacy.” China and fentanyl are different kinds of threats.

[Brad Findell @BradFindell]

@thomasahle @pgeerkens @solidangles @matthematician In the real numbers 0/0 is indeterminate whereas 2/0 is undefined. In the real projective line, 2/0 = ∞, 2/∞ = 0, and ∞/2 = ∞; but 0/0 is still indeterminate and we have more indeterminate forms: ∞ - ∞, ∞/∞, ∞ 0.

[Brad Findell @BradFindell]

@pgeerkens @solidangles @matthematician For the Ancient Greeks 0 was not a number but rather the lack of number. Many of our students think this way. (Ask them whether 0 is even, odd, neither, or both.)

As the concept of number expands, why shouldn't we call infinity a number? Cantor did.

[Brad Findell @BradFindell]

@pgeerkens @solidangles @matthematician Aristotle distinguished potential from actual infinity. Mathematicians often imagine a potentially infinite process has completed: e.g. 1/3 = 0.3333... only if we imagine an infinite string of 3's on the right.

Lakoff calls this the Basic Metaphor of Infinity.

[Brad Findell @BradFindell]

@Atheodosus @solidangles @matthematician The extended real line and the real projective line are both distinct definite entities. They contain all the real numbers and then one or two more numbers.

The former is topologically equivalent to a segment and the later to a circle.

[Brad Findell @BradFindell]

@lightediand @matthematician The real projective line, the Riemann sphere, and the extended real line all include the number that you circled. The extended real line also includes -infinity.

Cantor, of course, had lots of different infinities!

[Brad Findell @BradFindell]

@lightediand @matthematician Cantor would disagree.

[Brad Findell @BradFindell]

@littmath "Mathematics is queen of the sciences." Gauss

[Brad Findell @BradFindell]

@TomKenyon1 @drrajshah The students have already seen v'= Av as a shorthand for a transformation.

For a problem, it might be better to start in two dimensions. And the algebra is challenging, so might be motivating first to do a numerical example that works out nicely.

[Brad Findell @BradFindell]

@TomKenyon1 @drrajshah A seed of an idea:

[Brad Findell @BradFindell]

@MeidasTouch Misplaced modifier. You mean: "Trump removed, in May 2018, the regulations that would have prevented the Silicon Valley Bank crash last week."

[Brad Findell @BradFindell]

@alicekeeler @Mathgarden @MathTechCoach Most people quickly recognize vertical line symmetry, but the world is much richer than that.

[Brad Findell @BradFindell]

@alicekeeler @Mathgarden @MathTechCoach Key idea: A symmetry of a figure is a transformation that maps the figure onto itself.