Anna

Tutor math K-12+ and elementary reading || Taught high school math || Like rekenrek, cuisenaire, numicon

[_ @hveyhivrdcg]

クラインの壺を観測した

[Anna @oneplusepsilon]

@CmonMattTHINK I taught a class with that name. Some topics: number theory, recursion, special # sequences, generating functions, matrices & Markov chains; also Python for numerical exploration in problem sets. The problem-solving/writing/presenting was more important than any particular topic.

[Anna @oneplusepsilon]

@dodecahedra If you have surface area, then you can use the "tetrahedra" one to get volume from SA.

[Anna @oneplusepsilon]

@dodecahedra (We got volume before SA, e.g. #250 in https://t.co/mBcoJbaueq )

[Anna @oneplusepsilon]

@dodecahedra I think students understand sphere = sum of "square" pyramids more easily. The calculus of adding up the pyramid bases to get the SA of the sphere might be more intuitive. But I like how much there is in the orange peel method.

[Anna @oneplusepsilon]

@dodecahedra If you are measuring by displacement: since orange peels float, you need to measure the volume of whole orange, and subtract the volume of the peeled orange. That matches the mathematical process anyways!

[Anna @oneplusepsilon]

@dodecahedra Neat...I don't see how to change the radius & curvature physically. Are you interested in a different physical proof? You can peel an orange and use that (vol of shell) = (SA)*(thickness). (And you can actually do these measurements with beaker, graduated cylinder, caliper, etc.)

[Anna @oneplusepsilon]

@dodecahedra or a watermelon!

[Anna @oneplusepsilon]

@dodecahedra Or you can cut a small "square" pyramid out of a styrofoam ball, with vertex at the center, and use that (volume) = (sum of "square" pyramids vol) = 1/3*radius*(SA)

[Anna @oneplusepsilon]

@dodecahedra I think they're important for visualizing the "0/0" case of limits, including in the limit definition of derivatives. But if you can introduce limit notation while graphing rational functions in pre-calc, then it makes more sense.

[Anna @oneplusepsilon]

@a_mcsquared I agree the units are confusing! The unit would be the reciprocal of whatever the x-axis unit is. Then when you multiply to find area, that unit cancels and you get the fraction/percent of the population.

[Anna @oneplusepsilon]

@mathyawp I love the book Concrete Mathematics, at least for supplemental ideas even if it doesn't fit your needs as the main text:

https://t.co/EJyWLoryEw

[Anna @oneplusepsilon]

@MrEFinch

[Anna @oneplusepsilon]

@MathTechCoach You could also make models for volume:

[Anna @oneplusepsilon]

@MathTechCoach Students in a similar class made these Riemann sum puzzles:

[Anna @oneplusepsilon]

@ifgoldruste Tagging @Nicolak5mtr who might know about this. She has terrific ECAM-linked materials at https://t.co/unuj2PtUiL.

[Anna @oneplusepsilon]

@ifgoldruste I would like to know too! This is the closest I've found:

https://t.co/Zocog8Fab3

I haven't tried it since I just need a simple text resource like ECAM, not a digital system.