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Art and Mathematics

  1. Dec 24, 2007 #1
    I am a High School math teacher in the US, and our district is writing a curriculum for a new math class that will include a section on Math and the Fine Arts.

    I have found many websites that deal with this from a Fine Arts perspective, but we need some mathematical rigor in the class. Do you know of any texts or materials that include mathematics as the subject, instead of mathematics as a supplement to, Math and Fine Arts?

    Thank you in advance for any suggestions.
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  3. Dec 24, 2007 #2


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    I don't know if this is relevant to your project, but have you considered how manipulating fractal images might be "fine art"? I made these images using a program called Fractal Magic (available on-line from the author). The reason that I put "fine art" in quotes is that when I approached some art directors about maybe finding a commercial outlet for my work, they were less than enthusiastic. One worked for a place that did graphics for the music industry (CD liners, etc) and I was surprised about his lack of interest.



  4. Dec 24, 2007 #3


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    A few more:



  5. Dec 24, 2007 #4


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    Could you elaborate upon what this class is supposed to be?
  6. Dec 24, 2007 #5


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  7. Dec 24, 2007 #6
    It is a post Algebra 2 class (second year algebra) post geometry class, for seniors who need 4 math credits to graduate but are interested in a math / science / medicine career that would dictate a calc class. This class is directed to me mathematically rigorous, ie. covering and expanding upon topics found in Alg 2.

    The class is four quarters, one quarter of business/ finance/ personal finance, one quarter of math & fine arts, one quarter of computer applications, and one quarter of medical math. It is an "upside down" class, so we will be covering essentially the same math topics, geometry, polynomials, factoring, quadratics, exponential and logs, series, etc in all four quarters.

    The difficulty faced is to come up with the mathematical rigor. Math and Art is a common theme in many websites, but the mathematical rigor is not always present.
  8. Dec 24, 2007 #7
    I am sorry you met with such lackluster interest. I find fractals to be incredibly beautiful. They are definitely a topic of discussion in our class.

    You may want to check out the website "math-art" http://math-art.net/ , and specifically look at the piece entitled "At Peace". It is a landscape done entirely w/ fractals.

    Very beautiful.
    Last edited: Dec 24, 2007
  9. Dec 24, 2007 #8


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    I guess I meant my question more along the lines of "what do you mean by 'math and fine arts'?"

    Is the course meant to study artistic representations of mathematical objects (e.g. pictures of fractals)? Is it meant to study applications of mathematics to art (e.g. how to draw in perspective, or how to tune a piano)? Is it meant to look at mathematics itself as an art form? Is it meant to talk about something else?
  10. Dec 24, 2007 #9
    sounds like a class that will have problems like :

    "bobby has 5 paintings, he gives 3 paintings away and divides 1 painting in half. how many paintings does bobby still have?"

    i suggest you tell your district to take a hike.
  11. Dec 25, 2007 #10
    There is much confusion in this area. The reason you have problems finding mathematical rigor in the fine arts is because they really have very little to do with each other. What so many people fail to realize is that they embody completely different aesthetics. Fractals and the golden section are not Art, due to their beauty comes from the aesthetics of Mathematics not the aesthetics of Art. What math teachers need to teach is courses on the aesthetics of math and forget about art --- and vice versa. Now there is no reason that one can not use them in conjunction with each other however, one needs to know the differences between the two to do so.

  12. Dec 25, 2007 #11


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    Is it too late to change this?

    What did the folks that came up with this have in mind? Or <shudder> did they just create the section without any plans for what should be in it and why?
    Last edited: Dec 25, 2007
  13. Dec 25, 2007 #12
    No, that is not at all what this course is about. If you actually read my description, you would understand this.

    How about actually discussing and understand the equations that create the art. There is a lot of math in art. Look at the prints of Albrecht Durer. We will be discussing the Geometry in the prints. Or the math that gives the impression of perspective in art.

    There is a lot of mathematics that can be discussed, in depth, and with rigor. The artists who painted and created the art know this, but I guess you aren't interested in that.

    It is too bad that the narrow minded can't understand that.
  14. Dec 25, 2007 #13
  15. Dec 25, 2007 #14
    Dear Quantumduck,
    I didn’t mean to sound so negative in my first comment however, this area is one of my pet peeves. I realize that you are just looking for information and not interested in a debate on the aesthetics of mathematics and art. If you look at my blog you will find lots of information to get you started. If you look at the side bar on my blog and you will find a section on vismath. My guess is that this is what you are looking for as well as the work mentioned in last few blog entries. I also believe the most important link for your quest is the link to the Bridges conference on mathematical connections in art music and science. If you are in San Diego this January to attend the American Mathematical Society Conference you will see a MathArt show. This show is curated by members of the Bridges organization.

  16. Dec 25, 2007 #15
    Thank you very much, I will examine that.

    I didn't think you were that negative, others were definitely more negative. The goal of the class is to be a senior level class, that is not the normal, dry, never connect the mathematics to real applications, that is the normal state of affairs in high schools.

    Of course, what administrators and school board members don't understand is that the truly applicable math is calculus and beyond. That is where "real life application" truly lives.

    But, we have been charged with creating a different kind of math class to keep learners in math their senior year, instead of having them skip the fourth year of math (which is an option in my state) and then they end up in remedial math classes at University or Junior College because they didn't take 4 years of math.

    Teaching 4 quarters of applicable, rigorous, and topical math will make this course different enough to keep the learners engaged while still doing some tough algebra. That is the goal, and it is possible.

    Thank you, and all of the other people (yes, even Ice09) for your suggestions!
  17. Dec 25, 2007 #16

    now that i have more time to respond

    what you fail to notice is that many in this thread responded similarly to me because classes like this and proponents like you are what is systemically wrong with the math education in this country. by diverting your student's attention from the real math you are doing them a disservice. study series, sequences, convergence, and limits but forget the applications.

    most students are completely incapable of abstraction and ignorantly demand application because of classes like this. take note of the fact that this class you're designing would probably have bored to death many of the good mathematicians in this forum.
    Last edited: Dec 26, 2007
  18. Dec 27, 2007 #17
    Chaos comes to mind. Truly remarkable art is a matter of unpredictability, this need not mean absolute chaos; merely enough to, for want of a better word, deceive the layman.

    Personally fractals, geometric curiosities and the lot is just trivial mathematics. However one could consider the treatment of musical theory in the eyes of mathematics(deserving consideration first given by Euler), how Riemann's Zeta function is involved in such an aesthetically pleasing manner at the most unexpected instances.
  19. Dec 27, 2007 #18
    And what you don't realize, even after I have said it twice, is that this course is not for "good mathematicians". It is not for individuals who are going into calculus, and never will go into calculus.

    It is for the learners who would drop out of all math classes, stop taking math in high school, and say "screw it".

    So, your option is to let them drop out of math classes, fail at all math or be geniuses and enjoy the "drill and kill" because you enjoyed it.

    I guess that is why you teach college (I presume) and not high school. You are very out of touch with what it takes to actually educate learners in high school. I wish you great success, but if you don't really have anything interesting to add, why do you bother attacking me and my district?
  20. Dec 27, 2007 #19
    I can't help but agree with ice109, but this sort of mathematics teaching won't change overnight even if we disagree and keep quiet everytime an idea along its lines is put through. Besides it won't matter to the serious mathematicians(though I must say America is seeing less and less of those each generation, the wrong kind of push in academia of quantity over quality is largely to blame) for reasons quite obvious to such.
  21. Dec 27, 2007 #20
    then you were very unclear in your explanation of this class:
    no where did i suggest "drill and kill" whatever that is, and in fact i think drill and kill will be exactly what this class is your trying to build considering each section goes over the same exact topics. i don't teach anything, i'm simply a student in college who tutors and notices how the rest of his peers are doing.

    you are either setting them up for failure or setting up their college professors for failure. if you don't accept the advice given here by me and others go speak to a college math professor, preferably one taught in another country.

    you actually have a great resource in this forum because lots of people here have taught in one capacity or another(tutor, TA, professor) at the college level. ask and heed the advice about what they expect, need, want.

    obviously this a problem with the education ethic in the country and starts earlier than high school but there's no reason you shouldn't be attempting to mitigate it.
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