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If you have young kids (6 or 7) who understand multiplication and like math, Gauss's formula is such a magical thing to show them, because it seems like it'd be
by empath-nirvana 3y ago
If you have young kids (6 or 7) who understand multiplication and like math, Gauss's formula is such a magical thing to show them, because it seems like it'd be impossible to shortcut adding up all those numbers that way, on the surface, and it's such an easy thing to prove visually.
- nerdponx 3y agoHeck, it was magical to me when I first learned it in my 20s.
- godelski 3y agoThe other thing I like to show kids is how to count to a thousand (1023 to be precise) on their hands. Algorithm is simple, you just start from the outside of your hand (I use thumb as first position) and then to get a new inner most finger you must collapse all outward fingers. This is of course binary (00000, 00001, 00010, 00011, 00100, ...). Kinds love this and it feels like a super-power to them. Just be careful with teenagers because 4 has a problematic representation. But great way to discuss how counting systems and digit representation work. There's a nice puzzle too, that you can ask them how many "this" is with all fingers open. They usually need a hint, where you ask them how many an 11th finger would be. Funny thing is that kids usually pick up the counting system far faster than adults but adults tend to get the puzzle solved much faster.
- nonameiguess 3y agoIt generalizes to any arithmetic sequence. Intuitively, you're simply taking the average of all values (which is the midpoint for a sequence of evenly-spaced numbers) and multiplying by the number of values.
- 3abiton 3y agoHN never fails to surprise me