Conics in mathematics and geometry in particular is an import concept to understand.
We can take a cone and slice it to make a circle, line, point, ellipse and parabola.
But, can one take a piece of paper and fold it to make a ellipse, parabola and hyperbola? YES
In this lesson, you will fold a piece of wax paper to make these three shapes.
Proving the equation of parabola?
Visualizing how these three shape Ellipse, parabola, hyperbola are:
15 min. if just doing the folding.
Proof of a parabola Add another 30 - 60 mins
Playing with 2-D geometry to learn about conics!
Steps | Line Point | Circle Point | Circle Point |
---|---|---|---|
Draw shapes | |||
Fold | |||
Repeat Above |
EASY
EASY
Take care making the creases. The wax paper is not too forgiving.
Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.
It is also defined as the locus of all points equal distant from a given
point (our marker point) and a
line (our marker line).
When we drew a line and a point and folder the wax paper so that the line touched the marker point, we created a single point on the parabola. We can clearly see that the distance from the parabola point and the point on the line is equal to the point on the parabola and the marker point.
Now to prove that this is the formal for a parabola.
Now we just need a point to find the equation of the line y = mx + b
* The midpoint PL is where these two lines intersect.
* That is x = q/2 and y = 0
* 0 = q/2f * q/2 + b
* b = q**2 /4 f
* y = q/2f x + q^2 / 4 f or
* y = (q/2f)( x - q/2)
But wait we are not there yet!
y = (q/2f) (x- q/2 ) OR