24.09.09 Louis Jucker

Assignement no 1 | select a formal language of your preference

PARAMETRIC EQUATIONS CURVES ARE SEXY

equations curves are defined by algebraic expressions

these basic mathematical machines transform one information [x] into a new one [y]
combined together [x;y] these values create a dot
the sum of the dots draw a curve

beauty = fluidity + smoothness + logic

they are able to transform informations into forms

like architects do

PROPERTIES

equations curves share many properties with architectural forms

they like symetry

they have limits

they often repeat themselves

they respect maximums/minimums

the architect can control these forms by designing mathematical expressions
but this is a very complex method unless you're not a good mathematician

here's maybe an easier solution for architects

A GRAPHICAL METHOD

the tangent of any point on a curve is a linear function
it is the derivative of the curve's equation

vectorial drawing programs are already using tangents to draw curves (BEZIER paths)

maybe an architect could more easily manipulate equations curves if he would graphically integrate linear functions ?

this gives an idea of what the final curve looks like

this allows the architect to design complex forms by treating basic graphical informations

EXAMPLES ?

GAUDI used hyperbolic cosine curves to design SAGRADA FAMILIA | 1883

he used an empirical method to design these curves

the informations involved in this process are forces [N]
the forms are expressing static issues

today's buildings don't seem to care so much of gravity

forms should express different informations
such as densities - flows - environnemental values - etc