## MATHS with the robot

• SOME BASIC NUMBERS

Using a little Maths we can control the robot with a high precision in order to turn a number of degrees or to advance a distance.

a) The wheel diameter of the robot´s tires is 56 mm, so if you multiply by pi, you can verify the perimeter of the wheel and the robot moves a distance of 176 mm in each rotation that you have programmed.

perimeter of the wheel = diameter x pi = 56 x 3,1415 = 176 mm

For example, if you want to move a distance of 440 mm, the wheels need to rotates exactly 2,5 times. Students like to apply the "rule of three" in maths exercises and here is that they have to do!

b) In order to curve with precision, we can test with the Move Steering block of our software which is the exact number of degrees that both wheels have to rotate to turn a right angle, and in our experiments we decide they need to rotate 171 degrees.

So it´s easy to divide or multiply this number to obtain the equivalence with smaller or bigger angles in a curve, and we could fix the 30º- curve (57 degrees for the wheels) as  a module in order to move around polygons, to draw geometrical figures or to park the robot.

This is an example of how to move around a square with 220 mm of side:

CREATING POLYGONS

There is a rule in Maths which demostrates that "the sum of the measures of the external angles of a polygon is always 360 degrees"

By doing this operation 360/ number of sides, you can obtain the number of the  angle to curve with the robot. If you modify the previous program, you can easily move the robot around an equilateral triangle with this calculation:

360/3 = 120º so the wheels rotates 57 x 4 = 228 degrees

Or better, around a hexagon

HOW TO PARK THE ROBOT

In our next task we need to calculate the exact number of rotations to advance forward in four alternative moments (100 mm of distance = 0,57 rotations of the wheel), combined with three turns of a rigth angle (rotating 171 degrees), so this is the result of the program: