math-to-play-with  ...Because when we play, we learn!
    Math is hard for most of us. But things can be a little easier and more interesting if you can play with them.

    The pages you find on this website all illustrate basic math concepts —nothing advanced!— by letting you play with them.

    Be afraid no longer. Just play!!

    Title
    Description
    Geom.
    Trig.
    Number
    theory
    Stats
    Algebra
    Calc.
    Misc.
    Sneaking up on π with regular polygonsCompute π by fitting regular polygons (triangle, square, hexagon, etc.) to a circle. The more sides your polygons have, the more accurate and precise your computed π becomes.
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    eExplore the function f(x) = (1 + 1/x)x and see its limit of e.
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    N-gons and their anglesAs the number of sides and hence angles of a regular polygon increases, so do the size of the angles. However, the size of the angles does not increase linearly with the number of angles and cannot grow beyond a certain value.
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    N-gon triangulationThe sum of all (inside) angles of a polygon can be computed by dividing the polygon in triangles.
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    The Collatz conjectureTake any positive whole number. If it is odd, multiply it by 3 and add 1. If it is even, divide it by 2. Now repeat with the result and keep going. The series of results will always end with ...4, 2, 1 (repeating).
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    2D vector rotationDraw a circle, pick a point on the circle and draw a line from the center of the circle to the point you picked. Now rotate the point you picked along the circle a certain number of degrees (45°, 60°, etc.). What will be the coordinates (x, y) of the rotated point?
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    Sine, cosine and tangentExplore the basic sine, cosine and tangent functions.
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    CycloidsRoll a circle around the inside or outside of another circle and follow its trajectory.
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    Chromatic (12-tone) scale of musicCompare and listen to two versions of dividing up the (western) musical scale in 12 tones.




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    A simple derivativeEarly on in calculus we learn that the first derivative of a function is the slope of the line tangent to the function at any point (x, y). On this page you can play with functions of the type f(x) = xn and plot those tangents.



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    A simple integralIn calculus we learn that we can find the 'area under the curve' of a function by computing the function's integral. On this page you can play with functions of the type f(x) = xn and compute and plot those integrals.



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    Fibonacci seriesThe Fibonacci series of numbers starts with the numbers (1, 1). Each next number is the sum of the previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.
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    Triangle circlesDraw a triangle and its incircle and circumcircle (incircle is the largest circle we can fit inside the triangle; circumcircle is the smallest circle into which we can fit the entire triangle).
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    Kaprekar's constants — 6174 and 495Take a positive whole number of four digits; move the digits through a few steps and you always end up with the number 6174. Do the same with a three-digit whole positive number and the result will always be 495.
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    Pick's theoremIf you construct a polygon of which all border points have whole-number coordinates, Pick's theorem states that the area enclosed by that polygon can be computed simply from the number of whole-number points contained by that polygon.
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    The Mandelbrot setTake a (special) set of complex numbers and submit them to a simple, repeated process. For each of the numbers you picked see if it 'remains in the neighborhood' or 'escapes to infinity.' Paint all the ones that stay in the neighborhood white.
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    Can you hear me now?Plot the strengths of signals from two transmitters broadcasting at identical frequencies as their signals are received everywhere around them and marvel at the beauty and complexity of the result.




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    Sinusoidal SunPlot the (noon) angle of the Sun and the length of day for different latitudes on earth over the period of a full year.
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    Ulam spiral of primesIf you plot consecutive numbers in a spiral, prime numbers form spirals of their own.
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    Equations as matricesSolve pairs of simple linear equations with just a few matrix operations.


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    How many paths?Use simple matrix multiplication to find all the routes (paths) of a certain length between all locations.
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    The Monty Hall puzzleThe Monty Hall puzzle is a famous puzzle that has confused many. Although several solutions for it exist, here we use simulation as a means to explore the two strategies available when playing the puzzle.

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    The Petersburg paradoxThe Petersburg paradox involves the apparent paradox between 50% of something meaning one half of that something, and yet the difference between those 'halves' being quite large. It sometimes confuses those who gamble.

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    How long before we double or triple?Play with how long it takes for values to multiply if they grow at a constant rate.




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    Sum all (whole) numbers from 1 to NHow to quickly sum all (whole) numbers from 1 to N
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