Geogebra and functions (design)

The geogebra first design 

 

Our idea was to try to keep it simple, we made a scale model of what we wanted to make (a jar). We decided to include some curves to make it resamble as most as posible to a jar. So you could say that we first made the image and then made the math fit in. Due to the extension and shape of the sine we decided that would be our middle function or the "body" of the jar. Then we realized that the logarithm could connect with a softer curve in order to create the base. Finally we added the polynomial to make the top, almost cup like to finish the vase. This looked very beautiful in scale but had many problems when we tried to adapt it to solidworks, speacially because the shape of the sine changes depending on the period. So even though we planned we had to change it all over again. 

The geogebra second design 

Taking as base the first design we modificated the original functions instead of thinking "scale-like". The first and very obvious change was the sine's period, and from that by trial and error fitted again the other functions. That meant that we had to re-do the whole integral process and calculus but it was easier to translate it to solid works and then to rotate it.