What is beautiful to you?

Question

Combining e, π, i, 1, and 0 (arguably the five most important numbers in math) into one equation is elegant. Combining factorials and powers into infinite sums via a Taylor series to evaluate e or values of trig functions is amazing. Both of these circumstances bring a connectivity to mathematics that is beautiful to behold.

To me, one of the most beautiful things in math is that when the parabola is rolled along its curvature, the path of the parabola's focus creates a catenary... a link connecting quadratic equations to hyperbolic functions.

This is a personal opinion question... what in mathematics is beautiful to you?

Answer 1

For me, many things are beautiful in math. The derivative of a function is its tangent it is amazing. Finding that we can find the area under the curve integrating its function is amazing. How to find real values using complex variables.. without words. The knowledge of 'how and when to use' some hint, it is pleasant for us to find a result. We can find the values of e, π, etc. One and another time, using limits, integration, power series, convergence, etc.

But the most beautiful for me and I enjoy doing it, even if no one is asking me; it is to integrate functions.
If to derive a function is beautiful, for me, integrate it, is an art!

Answer 2

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I've always been intrigued by similar problems.... Back in hi-school, I began considering what I later learned to be the Golden Mean. I was fascinated with a proportion I discovered where 1/P = P-1. Quatratically, this becomes x^2 - x -1 = 0 which resolves to x = (sqrt(5) - 1) / 2.

Many years later I was reading a number theory book and was astounded to see the relation of this to the Fibonnaci series. It also explained how the series and the Golden Mean are expressed in nature and in the asthetic beauty of proportion found in art and the world.

I knew that I discovered something special in hi-school. I just didn't know what it was.

Answer 3

The first time I saw anything in mathematics that I described as "beautiful" was when I saw a full explanation of the Fibonacci numbers. Does anyone realize how prolific this idea is in nature? I mean...they're everywhere. They explain how shells form, how plants shoot off branches and at what heights, how ferns are really fractals in disguise, why the Greeks loved the golden ratio so much, why legal pads are both gold and in the golden ratio...it's just amazing. And all because some guy wondered what would happen to the population if you start with 2 rabbits and none of them ever died. Too cool.

Answer 4

My knee-jerk response was to say what Thomas F did, but this IS a mathematics question! No, I would have said you yourself.

(SPLASH of cold water)

Pi, the relationship between a circle's circumference and its diameter, is one beautiful thing I find in math because it represents infinite potential. Since pi is a transcendental number (it's got no discernible limit) and there's no apparent pattern the numbers form (3.14159265358979 . . .) despite having been carried out by hand and by computer to millions of places, that doesn't mean there ISN'T one, but we just haven't discovered it yet.

That's applicable to any great mystery of life (Is there a God? Is there life on other planets? What is the grand unified theory?); everything ultimately has a solution, but we haven't asked the right question or looked in the right place. Don't get fooled by people who say the numbers of pi or anything else is "random"; that means there is no discernible pattern -- but there is one, we just haven't found it yet.

Have a great day, and I'm glad you appreciate beauty in mathematics! So do I, among other things.

Answer 5

Actually it's my 2^a=3^b question. It's the foundation of why the circle of 5th (music) never repeats. From it evolves the musical scale, keys and harmony... Well, an anomaly in the human ear has a bit to do with the harmony thing too... But together one of the highest arts comes to life.

So, stepping back a bit further what does it mean? What link is there between math theory and art. Gives pause, yes?

Why are musicians also interested in math so much of the time?

Answer 6

Mathematics is the tool used to break physical phenomena into understanding. While e^ (i pi) -1 = 0 is EXTREMELY pretty, the uses of taylor series in understanding functions in which we cannot easily work with is so important in physics that one cannot say enough about it. If you want something pretty, look at a klein bottle sometime and try taking a trip to the otherside of it, oh wait, it has only one side.

Answer 7

To me the most beautiful and fscinating concept in mathematics is the Indo Arabic way of representing the numbers in decimal system but for which even Albert Einstein would have failed in Arithmetic.
Try multiplying 948 and 793 writing them in Roman numerals.
Try to find out a simple method for subtraction in Roman numerals.I swear, you will quit mathematics.

Answer 8

I find two things most beautiful in math, however it's not necessarily their mathematical operation that defines their beauty to me but their everpresence on earth that does.

1.) Fractals: Nothing to me is more beautiful, or zen-like, than visualizing fractal representation. Being that I look at A LOT of charts (IE maps) in my job, I always find my mind wandering to thinking about what the shoreline of the land would look like at different magnitudes.

2.) Phi: I have always been fascinated by the presence of Phi around us, from natural bodies to great works of art to human characteristics, I've always been fascinated by this ratio.

Answer 9

ive always been fascinated by quadratic and simultaneous equations---the base of solving almost everything in math.im an engineering student and study advanced math, but still am amazed about elementary stuff...including the invention of pi, the pythogras theorem...the progressions and and above all calculus


by the way ur legs are daaaaaamn cute:)
please dont tease like that

Answer 10

The balance in math is beautiful. When the balance is level, then answers are found. And math is not the only thing that tries to balance the scale. Nature tries to balance it too. When one person does something for another person, that person expects something back, always, either from the person or somehow in points on God's check list.