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# More Basics

Solving this set of exercises increases your skills in algorithmic thinking and Python’s syntax. Everything you need has been discussed in the Crash Course chapter. Do not use additional Python features or modules.

## Point Inside Rectangle?

Get two integers from the user and check whether the corresponding point lies inside the rectangle with corners at (-1, -1), (5, -1), (5, 2), (-1, 2). Print a message showing the result.

Solution:

    # your solution

## Square Numbers

Get an integer from the user and tell the user whether it’s a square number or not. If you want to compute square roots, use `123 ** 0.5`. Print a message if the user gave a negative number.

Hint: Have a look at the output of `16.125 % 1`.

Solution:

    # your solution

## Unique Items

Write a function `no_duplicates` which returns `True` if the passed list contains no duplicates and `False` if there are duplicates.

Test your function with `[1, 4, 5, 6, 3]` and `[1, 3, 1]` (and with `[]`, of course).

Solution:

    # your solution

## Increasing Subsequence

Write a function `inc_subseq` which takes a list of numbers and prints all items except the ones which are smaller than their predecessor.

Test your function (at least) with `[1, 3, 2, 3, 4, -2, 9]` and `[3, 2, 1]`.

Solution:

    # your solution

## Area of a Circle

Get an integer radius of a circle from the user. Calculate and print the circle’s area as well as the edge length of a square with identical area. Check user input for validity. You may use NumPy’s `pi` constant.

Solution:

    # your solution

## Quadratic Equations

Solve the quadratic equation \(a\,x^2+b\,x+c=0\) with user-specified \(a\), \(b\), \(c\) (integers). Give all real solutions.

Solution:

    # your solution

## Regular Polygons

Use Matplotlib and NumPy’s `sin` and `cos` functions to plot a regular polygon. Ask the user for the number of vertices and check user input for validity.

Hint: For \(n\) vertices the \(k\)th vertex is at \((\cos\varphi,\sin\varphi)\) with \(\varphi=2\,\pi\,\frac{k}{n}\).

Solution:

    # your solution

## Stars

Draw a star with user-specified number of outside vertices. Radius for inner vertices is 0.3, for outer vertices it’s 1.

Solution:

    # your solution