Greetings my dear friends of the Hive.blog platform, especially to the members of the friendly community of @project-hope, in fact it will always be important to highlight the essential influence of each technological application in our lives, with it have been provided countless machines, tools or devices created by man in order to carry out a particular purpose, and this we have been able to verify in each of the previous articles.

This time I want to talk about a wonderful technological application that allows us to make countless curves or geometric shapes such as straight lines, circles, parabolas, ellipses, among many others, and also these geometric figures can make gif type, this time I wanted to carry out the realization of a wonderful curve known in the mathematical-physical world as cycloid, this impressive curve is generated through a point that is on the edge of a certain generatrix circumference, and it rotates without sliding on a flat surface.

Referring a little to this curve we can say that in its beginnings it was considered the Helen of geometry (Helen of Troy of Greek mythology) or of the curves, either by its interesting formation or simply by all the controversy that it generated during its beginning, to summarize, the cycloid when inverted turned out to be the shortest path that can travel a given mobile starting from a point A to another B, and even faster than a straight path at the same initial conditions, without thrust, under the effect of gravitational action and without friction.

For this reason I wanted to generate a cycloid using GeoGebra as a fundamental tool for the conformation of any geometric figure and also with movement, for this let's start with the steps in a general way as you can see below:

Step 1: Open GeoGebra

Step 2: Create a slider

Step 3: In the same creation of the slider we go to animation and select that the movement originates in an oscillating way

Step 4: Now we create the point (C) that represents the center of the generating circumference of our cycloid

Step 5: Then we choose our circumference which already has its center and from there we can trace its radius

Step 6: Now we locate our generating point of the cycloid, remembering that it will rotate with the generating circumference without sliding

Step 7: Then, so that our point at the edge of the circle can rotate with the circle, we select the angle and direction of rotation

Step 8: Then we indicate where the turning point will start and where it will end and in which direction

Step 9: By moving our slider our point on the edge of the circumference will rotate at the same time as the generating circumference of our cycloid as you will see

Step 10: As we want to draw a cycloid, we activate marking the locus of this figure

Step 11: For this we indicate the point at the edge of the circumference to the slider and in this way our cycloid is generated in a synchronized way

Step 12: With the invisible label option we can hide elements such as the angle, points, among others

Step 13: For our gif we proceed to go to file, export, graphic view to animated gif

In this way we will obtain the wonderful cycloid curve using Geogebra as a technological tool, later we will be observing that we can make other impressive curves such as epicycloids and hypocycloids and we will know in a general way certain aspects about them.

Until another opportunity my dear and appreciated readers.

Note: All images were obtained from the GeoGebra application and worked on in Power Point.

Recommended Bibliographic Reference

[1]GeoGebra

[2]Cycloidal movement. Author: @rbalzan79