### Turtle calculus

Its easy to plug in various functions as a graph's gradient in Turtle Art. The resulting graph is the integral of the function used as the gradient. In the below case, the gradient is 1 and its integral is a straight line, f(x)=x

Plug in a linear gradient, -2+x/100, and make a parabola with zero crossings at x=0 and x=400

A quadratic gradient generates a cubic with zero crossings at x=0 and x=300

The integral of sin is -cos

(by the chain rule)

making dy/dx =y gives an exponential curve

but a nonzero value at x=0 is necessary, in this case forward 1 means f(0)=1

starting at 0, f(0)=0 has a solution of a straight line f(x)=0

Challenges

Graph for negative x

Graph the exponential for f(0)=-1 explain

The exponential above is for dy/dx = y/100 what exactly is the formula for the graph?

Find more interesting integrals

Graph the derivative of a function

Iteratively solve d2y/dx2 =-y

Explain the offset in the graph of -cos

A step size of 1 is used, what error does the step size introduce?

Plug in a linear gradient, -2+x/100, and make a parabola with zero crossings at x=0 and x=400

A quadratic gradient generates a cubic with zero crossings at x=0 and x=300

The integral of sin is -cos

(by the chain rule)

making dy/dx =y gives an exponential curve

but a nonzero value at x=0 is necessary, in this case forward 1 means f(0)=1

starting at 0, f(0)=0 has a solution of a straight line f(x)=0

Challenges

Graph for negative x

Graph the exponential for f(0)=-1 explain

The exponential above is for dy/dx = y/100 what exactly is the formula for the graph?

Find more interesting integrals

Graph the derivative of a function

Iteratively solve d2y/dx2 =-y

Explain the offset in the graph of -cos

A step size of 1 is used, what error does the step size introduce?

Labels: calculus, maths, olpc, Sugar, TurtleArt, TurtleBlocks

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