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This is kind of a plea for help - how can I learn maths 'via' geometry? I just can't get my head around 'numbers'. I can't seem to really visualise them or und

This is kind of a plea for help - how can I learn maths 'via' geometry? I just can't get my head around 'numbers'. I can't seem to really visualise them or understand what they are. I know this sounds weird. With language or abstract things like 'problems' I can almost see them in my head. I can analyse a problem and all it's flows of cause and effect in a visual way. That's literally what happens in my head. But with numbers I can't understand them at a basic level. Like - what are they? How do I visualise them? When it comes to geometry it's almost like it's the 'language' of my brain, how I think, in terms of shape and form and translation and dimension. I'll give you an example. I learnt Pythagoras theorem aged about 13 or something. But didn't truly understand it until I was about 20 something when I saw a diagram showing graphically the squares of the sides like this[0]. I really need to start at the absolute beginning, like build of a whole foundation of what maths is based on geometry. Does that even exist? This might not be possible, but if I can even get started it would be great. [0] https://mysteriesexplored.files.wordpress.com/2011/08/pythagoreantheorem.png https://mysteriesexplored.files.wordpress.com/2011/08/pythag...

earthicus 8y ago
If you managed to survive high school algebra, you might be able to 'redo' your basic math education with a geometric bent from Stillwell's book 'Numbers and Geometry', which teaches the classical link between the two subjects that has been eliminated from elementary education to some extent. However, the kind of intuition he presents is still semi-abstract - it's not a super duper picture heavy book - but I think it's about as close to what you're asking for as you are likely to find. https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-Mathematics/dp/0387982892 https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-...
abecedarius 8y ago
Just one suggestion, but https://www.euclidea.xyz/ https://www.euclidea.xyz/ is a great place to start. Visual Group Theory sounds appropriate too: https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/0...
empath75 8y ago
Have you watched the khan academy videos? He leans on geometry and visual intuition quite a lot.
brianpgordon 8y ago
I think this is a better image for the Pythagorean theorem: https://i.imgur.com/UxZ3fQR.png https://i.imgur.com/UxZ3fQR.png
PinkMilkshake 8y ago
I think I know what you are getting at. You may have something like dyscalculia[1], but I'm not a doctor. There are several mental models used for picturing numbers. I think the most popular is the number line [2]. Common Core uses this in a clever way. I've never found it useful personally. I suspect some people might see numbers as purely symbolic and perform purely symbolic operations. When the symbol 2 and the symbol 3 have the operation 'add' applied, it yields the symbol 5. Or something. I think I mostly visualize the numbers as a quantity of solid objects. So I think of 3 as 3 things. This has limitations. I can break objects apart but how do you visualize 3.767? So some of it is intuitive. There is evidence that the human mind can only encode exact quantities up to four [3], after that they use an estimate. [4] So maybe your situation is the norm. What I mean is, sometimes it can feel like everyone else has 'got it' and you're the one lacking, when in reality everyone is just as bad. [1] https://en.wikipedia.org/wiki/Dyscalculia https://en.wikipedia.org/wiki/Dyscalculia [2] https://en.wikipedia.org/wiki/Number_line https://en.wikipedia.org/wiki/Number_line [3] https://en.wikipedia.org/wiki/Parallel_individuation_system https://en.wikipedia.org/wiki/Parallel_individuation_system [4] https://en.wikipedia.org/wiki/Approximate_number_system https://en.wikipedia.org/wiki/Approximate_number_system

earthicus 8y ago

If you managed to survive high school algebra, you might be able to 'redo' your basic math education with a geometric bent from Stillwell's book 'Numbers and Geometry', which teaches the classical link between the two subjects that has been eliminated from elementary education to some extent. However, the kind of intuition he presents is still semi-abstract - it's not a super duper picture heavy book - but I think it's about as close to what you're asking for as you are likely to find. https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-Mathematics/dp/0387982892 https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-...

abecedarius 8y ago

Just one suggestion, but https://www.euclidea.xyz/ https://www.euclidea.xyz/ is a great place to start. Visual Group Theory sounds appropriate too: https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/0...

empath75 8y ago

Have you watched the khan academy videos? He leans on geometry and visual intuition quite a lot.

brianpgordon 8y ago

I think this is a better image for the Pythagorean theorem: https://i.imgur.com/UxZ3fQR.png https://i.imgur.com/UxZ3fQR.png

PinkMilkshake 8y ago

I think I know what you are getting at. You may have something like dyscalculia[1], but I'm not a doctor. There are several mental models used for picturing numbers. I think the most popular is the number line [2]. Common Core uses this in a clever way. I've never found it useful personally. I suspect some people might see numbers as purely symbolic and perform purely symbolic operations. When the symbol 2 and the symbol 3 have the operation 'add' applied, it yields the symbol 5. Or something. I think I mostly visualize the numbers as a quantity of solid objects. So I think of 3 as 3 things. This has limitations. I can break objects apart but how do you visualize 3.767? So some of it is intuitive. There is evidence that the human mind can only encode exact quantities up to four [3], after that they use an estimate. [4] So maybe your situation is the norm. What I mean is, sometimes it can feel like everyone else has 'got it' and you're the one lacking, when in reality everyone is just as bad. [1] https://en.wikipedia.org/wiki/Dyscalculia https://en.wikipedia.org/wiki/Dyscalculia [2] https://en.wikipedia.org/wiki/Number_line https://en.wikipedia.org/wiki/Number_line [3] https://en.wikipedia.org/wiki/Parallel_individuation_system https://en.wikipedia.org/wiki/Parallel_individuation_system [4] https://en.wikipedia.org/wiki/Approximate_number_system https://en.wikipedia.org/wiki/Approximate_number_system