Sunday Afternoon Maths XX

 Posted on 2014-07-13 

Bézier curve

A Bézier curve is created as follows:
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).
\(n\)) 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:
$$P_0=\left(0,1\right)$$ $$P_1=\left(0,0\right)$$ $$P_2=\left(1,0\right)$$

Show answer & extension

Folding A4 paper

A Piece of A4 paper is folded as shown:
What shape is made?

Show answer & extension

If you enjoyed these puzzles, check out Advent calendar 2019,
puzzles about 2d shapes, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


trigonometry irreducible numbers chess proportion crossnumbers digital clocks dodecagons shapes palindromes dominos elections addition division crossnumber multiplication 2d shapes probabilty quadratics christmas odd numbers symmetry regular shapes perimeter averages calculus range coins area money time ellipses remainders bases parabolas probability 3d shapes balancing coordinates lines prime numbers numbers doubling differentiation cryptic crossnumbers cube numbers sequences median sums colouring chocolate factorials menace products integers triangles routes functions rugby folding tube maps mean volume integration triangle numbers factors planes arrows grids books fractions digits indices circles sport chalkdust crossnumber means dates star numbers tiling polygons hexagons partitions rectangles floors square roots spheres clocks angles gerrymandering geometry dice speed ave shape cryptic clues percentages squares square numbers unit fractions graphs wordplay sum to infinity cards taxicab geometry perfect numbers surds complex numbers crosswords games logic pascal's triangle advent people maths number scales multiples algebra the only crossnumber


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020