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This is a pretty straightforward way to visualize the points on a set of axes. The origin would be your starting point, or simply a reference point that you call zero. Because it is visual, it would be better as either a video or an interactive widget.

I will admit that the colour system seems a bit unusual to me because I've always just understood math the way it was taught at school, in abstractions as you mentioned. But I'm open to learning more, and if it's more intuitive and visual, then it could be very helpful to others.

I agree that colours should only be used to understand the concept, as obviously not a lot of people instantly think of them when solving problems. I would suggest looking at math books that you like and experimenting with the number of examples, using the feedback of other people to guide you.

Don't use Word; it's not good for marking up equations. Overleaf is an online LaTeX editor which will be easy to set up and use. There are also other distributions that run locally on your computer.

The colour system works well with visualizing graphs and spatial objects imo. Also I don't see how Riemann sums are relevant? I encountered them in calculus, not algebra.

I would visualize higher-order polynomials by analyzing the parts. In your example, 4x + 4x^2 + 4x^3 = y could be thought of as a product of y = 4x and y = x^2 + x + 1. You could substitute x with random values on the domain and see if their product would be negative, positive, or zero. Then the graph is a bit more visible. Just by inspection, I can tell that it's going to be an increasing cubic function.

I can see where this comes from but I advise against thinking of the trig functions as simply how they are placed on the coordinate plane. At their core, they are relationships between side lengths of a triangle. Also it seems that the associations between the trig functions and colours are for the unit circle (r = 1). I'd be interested to see how it could be generalized for any r.

0-9 are the digits because we use the decimal system. The tens place indicates how many tens are there in a specific number. 10 is understood to be one ten as there is a one in the tens place. The rightmost column is the ones place value, which indicates how many ones are there in a number. e.g. 19 means there is one ten and nine ones, which checks out as 1 * 10 + 9 * 1 = 10 + 9 = 19. I prefer using cubes to visualize this as I find that others usually group them in tens.

For the fractions, isn't it enough to divide a whole into equal parts (as indicated by the denominator) then shade in the number of parts (as indicated by the numerator)? For example, 3/4 means cutting a whole into 4 equal parts, then shading in three of them. Most people are able to draw a picture of this. I don't see how colour would play a role in this case. Maybe it could, but it seems odd to reinvent the wheel.

It does seem like you have a lot of ideas and enthusiasm for sharing math with others, which is awesome! I would suggest picking a fundamental concept and building up your explanations or colour system from that. I think it would be better as an entire set of digital lessons with videos and/or interactives rather than a book.

I do think that there is potential in the visualization of axes, but I think it would be best to stick with the Cartesian plane where there's only two variables. It could be extended to three axes and beyond, but imo it seems pointless unless you are teaching multivariable calculus, vector calculus, or any other field that deals with transformations in higher-dimensional space, like linear algebra in R^n.

New ways of understanding math are really interesting for me so I'd be glad to hear your thoughts!
 

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The colours seem to relate to how numbers are presented rather than a new way of understanding concepts. The examples you've listed can all be understood without the colours, though might be less engaging indeed. It works so it should be fine.
 

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Sounds like you've got a great idea.

Make calls to related organisations, but anyone who knows about it can make their own version of your book and plagiarized it wilfully.

According to a US government website "Copyright, a form of intellectual property law, protects original works of authorship including literary, dramatic, musical, and artistic works, such as poetry, novels, movies, songs, computer software, and architecture. Copyright does not protect facts, ideas, systems, or methods of operation, although it may protect the way these things are expressed"


The best thing you can do is write up a non disclosure agreement with the statement "the signee of this document agrees to not share any idea, concept, content or related matter" to "any other party other than the author of the work".
Then get their signature, to make the document binding. Then send it to private organisations to publish it or to find a publisher.

I'm sure there are organisations that can help writers all over the world you can send it to,but you would have to have them sign the NDA (non disclosure agreement)

Actually this whole thread is not the best idea because now anyone can plagiarize your concept or ideas and make related versions of the book you want to publish and have legal right to do so.

Not even in equity law would you be able to argue that this information was shared in confidence or in private and, could be restricted because as an online forum this is an open space for anyone to share or retain other's ideas.(in other words, they can steal it as part of a public domain) Unlike social media messaging between friends which would be considered to have been shared in confidence and such designs or creative works, can be restricted in an equity court of law. So your friends can be sued for stealing confidential information or a creative work, but not the whole internet who has access to this forum.
 

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I figured id might as well show some examples so i can illustrate what im describing .
For the fundamental math these where the colors i chose with the corresponding shapes ( granted some may change in future )
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A worked out example , in this one we are given a list of numbers to add together . i use a kinesthetic approach on my examples as well as colors.
here i first identfied the unites , then i colored them to make it more apparent of the units . Below that you see rectangles /w orange dots . This stems from a contrapation that will spit out ones if they are 9or less. 10 of these rectangles make up a square and fit into the "square box " which is 100 units . so if needed some one could physically build the equation to solve it , which gets your hands eyes and is more of a game for solving and things correspond so its not ambiguous . then you see i added things together and get a solution .It may look strange at first and seem over whelming but if you had blocks you'd pick up the colors pretty quickly . i was trying to design it such that if someone who does not understand the properties of decimals would not be able to put pieces together where they did not belong hence the ejecting ones out from the tens example i eluded to earlier.
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This is an example of Divsion , this one kicked my but when i was trying to think of a way of incorperating blocks and an idea for some one else to follow but i believe i have solved that issue at least for myself and in my mind .
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The next image is a solution path using the colors for division , granted this type of reasoning might not be great for everyone .but it illustrates several key factors in how the equation works from its most basic form and questions id have asked such as the numbers on top ( which is why i am showing the zeros as place holders for each unit we are solving for ). I think this looks better than black & white lettering.
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Here is a terrible example i quickly wrote up for fractions , but i think people can see the reason i thought it might be a good idea because a large issue is with matching denominators for addition and people just don't see it . i think with this method they can see the denominators not matching ( i think this style is good way for instructional purposes and for tutoring as well take home notes so if a student so wishes they can folow the color coding . i by no means exepect others to use these colors only but i do think that there should be many examples with these colors so people can follow a patern if they are trying to read a book for help / follow work .
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For Cartesian plane here is an image of the axis
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what is interesting about this method is if you do it long enough you start seeing numbers in colors based on their place value even if the letters are black its kinda cool .i will follow this up with one more post .
~+~
Get a copyright over this before someone steals your designs
 
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