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# Doodling in math: Infinity elephants

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• At on the video she mentions that these drawings show "the smallest countable kind of infinity". Can anyone recommend a nicely approachable explanation of the kinds of infinity out there?
• There are both countable and uncountable kinds of infinity. This comes from an area of mathematics called set theory. There is a nice explanation here: http://www.youtube.com/watch?v=WihXin5Oxq8
• At , who is Mr. Tusks?
• Mr. Tusks is an elephant in Dinosaur Comics. He is afflicted by island dwarfism and is the Vice-Mayor of Tiny Towne.
• Around , she mentions that a circle can be defined by any three points. What if the three points were in a straight line?
• The case you gave is the ONLY exception
A circle can be defined by ANY three non-collinear points.
Call them A, B, C
Join AB and BC
Draw perpendicular bisectors of AB and BC
The bisectors meet at the center of the circle
• At , does she say" some thing something something if the next phrase is twice as fast?" Any way nice video!
• "Well, I have an infinite amount of information I'd like to share with you in this last sentence, and I can still do it in the next 5 seconds if i say the next phrase twice as fast, and the next one twice as fast as that, and the next one twice as fast as that" and so on.
• Wikipedia isn't always reliable, but you might be right.
• What would happen if you drew circles within the circles already drawn? Does it break the main concept of the idea?
• Well, you can draw circles within circles, like the Apollonian Gasket at , but you have to draw the two biggest circles that fit inside the first circle. If you draw the biggest circle-inside-a-circle that could possibly fit inside the first one, it will be almost the same size as the first circle, and you won't be able to differentiate between the first circle and the second one, because they will both be about the same size. Or you could do concentric circles, like the orbits of planets or rings on a bulls-eye.
So to answer your question, you can draw circles within circles, but it works out best if you do more than one biggest circle inside the main circle, or concentric circles.
I also just like using the word concentric.
--Blue Leaf
• she says that circles can be defined by three points, can't a circle be defined by more than three?
• No. A circle is only defined by three points. If you have three points, then there is only one circle that can pass through all three (unless they are collinear in which case no circle can). A fourth point would either be redundant or make the circle previously defined invalid.
• What does she mean with an infinite series that aproaches one? How can something infinte approach a normal integer?
(1 vote)
• An infinite series is not necessarily infinite. An infinite series is really a sum of an infinite number of terms. Some terms may be negative, causing cancelling. Some terms may be small enough to fit within the area remaining.
• What if instead of trying to fill up an organic shape with a geometric shape, you tried to fill up a geometric shape with an organic shape? (like elephants inside of a circle.) Do you think it'd still be as fun?
• why is infinity such a big deal anyway
• Infinity is able to help in math in cases such as this. It is able to explain things that would be impossible otherwise. For something that's 'not-a-number', it's a pretty good number.
(1 vote)