Chat with a (~13yr old) student on Friday that I want to turn to "interesting maths", rather than the classes they don't like.
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Chat with a (~13yr old) student on Friday that I want to turn to "interesting maths", rather than the classes they don't like. Thinking about infinity...Hilbert's Hotel and countable v uncountable (natural v integers v real etc).
Any ideas on that theme for that age? -
Chat with a (~13yr old) student on Friday that I want to turn to "interesting maths", rather than the classes they don't like. Thinking about infinity...Hilbert's Hotel and countable v uncountable (natural v integers v real etc).
Any ideas on that theme for that age?@_thegeoff
The (don't say four) color theorem (have them experiment with finding max no of colors on their own).Adding powers of two. Spot the pattern. (Try to) prove it.
Wrap a string around a tennis ball. How much more string do you need to keep a distance of 2 cm to the ball all around? For a basketball? Planet Earth? Proof?
Pose the Bridges of Königsberg.
Sum of angles in a triangle. If they haven't learned, let them draw random triangles and measure. Why? What happens on a sphere?
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N niels@social.data.coop shared this topic
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Chat with a (~13yr old) student on Friday that I want to turn to "interesting maths", rather than the classes they don't like. Thinking about infinity...Hilbert's Hotel and countable v uncountable (natural v integers v real etc).
Any ideas on that theme for that age?@_thegeoff Perhaps "what is the square root of minus one?", imaginary(!) numbers and "numbers as something with an angle and a length"
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@_thegeoff
The (don't say four) color theorem (have them experiment with finding max no of colors on their own).Adding powers of two. Spot the pattern. (Try to) prove it.
Wrap a string around a tennis ball. How much more string do you need to keep a distance of 2 cm to the ball all around? For a basketball? Planet Earth? Proof?
Pose the Bridges of Königsberg.
Sum of angles in a triangle. If they haven't learned, let them draw random triangles and measure. Why? What happens on a sphere?
@_thegeoff
Dimensional analysis. Why aren't mice and elephants the same? Why are large ships more efficient?Sierpinskis triangle, Cantor set. Box dimension (related to dim analysis above). Non-integer dimension.
Orientation of surfaces. Möbius strip, Klein bottle.
Some of these ideas are for a rather precocious 13-year old, some of them could work with individual adjustment. Be prepared to have no purchase, you can't force this. Only slightly related to (un)countable sets.
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@_thegeoff Perhaps "what is the square root of minus one?", imaginary(!) numbers and "numbers as something with an angle and a length"
@nichni Complex stuff probably requires skills that aren't available (I'm trying to at least encourage maths as a subject where it's been rejected cos, my words, "maths is just sums and is boring"). Vectors is interesting, we've done some wave interference via electric guitar science stuff, which is how this all got started.
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@_thegeoff
Dimensional analysis. Why aren't mice and elephants the same? Why are large ships more efficient?Sierpinskis triangle, Cantor set. Box dimension (related to dim analysis above). Non-integer dimension.
Orientation of surfaces. Möbius strip, Klein bottle.
Some of these ideas are for a rather precocious 13-year old, some of them could work with individual adjustment. Be prepared to have no purchase, you can't force this. Only slightly related to (un)countable sets.
@niels Fractal stuff is interesting...
This is for a student who has kind of rejected maths at high school level, I get the impression they think it's just sums and they're not very good at sums. So no huge maths specific skills, but still plenty of curiosity and smarts. -
@_thegeoff
Dimensional analysis. Why aren't mice and elephants the same? Why are large ships more efficient?Sierpinskis triangle, Cantor set. Box dimension (related to dim analysis above). Non-integer dimension.
Orientation of surfaces. Möbius strip, Klein bottle.
Some of these ideas are for a rather precocious 13-year old, some of them could work with individual adjustment. Be prepared to have no purchase, you can't force this. Only slightly related to (un)countable sets.
@_thegeoff
Also, let them geek out about what they're interested in. You have wide interests, there could be overlap, then take it from there. Build relationship first, then worry about maths later. You might of course already have done that, I have no idea. -
@nichni Complex stuff probably requires skills that aren't available (I'm trying to at least encourage maths as a subject where it's been rejected cos, my words, "maths is just sums and is boring"). Vectors is interesting, we've done some wave interference via electric guitar science stuff, which is how this all got started.
@_thegeoff
Well then Fourier analysis, you have your infinite sums right there. Best if you can find some nice apps for splitting sounds into overtones and reverse. Make electronic music, get famous, retire on proceeds.I saw at some point an online app for constructing vowels from formants and two overtones, kinda nice.
@nichni -
@niels Fractal stuff is interesting...
This is for a student who has kind of rejected maths at high school level, I get the impression they think it's just sums and they're not very good at sums. So no huge maths specific skills, but still plenty of curiosity and smarts.@_thegeoff @niels
What about logic? Starting with boolean then going on to predicate.
(Incidently I see they've changed the symbols since I first learned it) -
@_thegeoff @niels
What about logic? Starting with boolean then going on to predicate.
(Incidently I see they've changed the symbols since I first learned it)@HighlandLawyer @niels Already done it! We built a very basic transistor amp, and that lead from analog to digital electronics, and booleans, logic gates, Minecraft and number bases / binary logic.
(Now that I mention all the stuff we've covered since "can you chat to this student about science, but from the perspective of something they like, such as electric guitars", it does seem to have snowballed a little.)
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@HighlandLawyer @niels Already done it! We built a very basic transistor amp, and that lead from analog to digital electronics, and booleans, logic gates, Minecraft and number bases / binary logic.
(Now that I mention all the stuff we've covered since "can you chat to this student about science, but from the perspective of something they like, such as electric guitars", it does seem to have snowballed a little.)
@_thegeoff
Careful now, or you'll be authoring papers together...
@HighlandLawyer
