Practice Problem 1
Write the function minimum(number_1, number_2) that
returns the minimum of the two parameters, number_1
and number_2. The function should not use the
built-in min function.
Practice Problem 2
Write the function clamp(number, minimum, maximum) that
returns the result of clamping the specified number into the range
$$[minimum, maximum]$$. That is, if number is below
minimum, it returns minimum,
if number is above
maximum, it returns maximum, and otherwise
it returns number. The function should not use the
built-in functions min and max.
Earlier this semester we estimated pi using the Leibniz approximation. Another way of estimating the value of pi is to use Monte Carlo Estimation. The technique is named after the casino because it depends on random chance and probability. Before you can use the technique to estimate pi, you need a test for whether a given point is inside of a circle.
Details
In a file called point_in_circle.py, write a program that allows the user to click in the window and draw small points. The color of the points should be determined by whether or not the point is located inside of a larger circle. If the point is inside the circle, the point should be drawn in green, if the point is outside the circle the point should be drawn in red. Consider a point on the line to be inside the circle.
Example Output
Hint
-
A point is inside of a circle if the distance between the point and the center of the circle is less than the radius of the circle.
The distance between two points can be computed using the Euclidean Distance formula:
$$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$
Where \(d\) is the distance between the points \((x_1, y_1)\) and \((x_2, y_2)\).
-
You can
use
graphics.wait_for_button_press()to force your program to wait for the user to press a mouse button. -
You can use the
xandyfunctions to get the coordinates of the mouse click.
Challenge
To perform a monte carlo estimation of π, we need to estimate the area of the circle. Create a square window in the graphics module, and draw a circle centered in this window as large as possible. Generate a large number of random points, and keep track of which ones end up in the circle, versus the total number of points generated. We can then estimate π using the following equation:
\[ \pi = \frac{4 \times points\_in\_circle}{num\_points\_generated} \]Submission
Please show your source code and run your programs for the instructor or lab assistant. Only a programs that have perfect style and flawless functionality will be accepted as complete.