Sunday Afternoon Maths XX

Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit.

Folding A4 Paper

Source: ATM Mathematics Teaching 241 (July 2014)

A Piece of A4 paper is folded as shown:

What shape is made?

Bézier Curve

A Bézier curve is created as follows:

Image source: WikiPedia

1) A set of points $P_0$, ..., $P_n$ are chosen (in the example $n=4$).

2) A set of points $Q_0$, ..., $Q_{n-1}$ are defined by $Q_i=t P_{i+1}+(1-t) P_i$ (shown in green).

3) A set of points $R_0$, ..., $R_{n-2}$ are defined by $R_i=t Q_{i+1}+(1-t) Q_i$ (shown in blue).

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$n$) After repeating the process $n$ times, there will be one point. The Bézier curve is the path traced by this point at $t$ varies between 0 and 1.

What is the Cartesian equation of the curve formed when:

$$P_0=\left(0,1\right)$$ $$P_1=\left(0,0\right)$$ $$P_2=\left(1,0\right)$$