In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditchcurve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations
$\displaystyle x=A\sin\left ( at+\delta \right )$
$\displaystyle y=B\sin\left ( bt \right )$
which describe complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857.
— "Lissajous curve" From Wikipedia, the free encyclopedia
With this definition in mind, below is a gif of some interesting 3D Lissajous curves on a sphere.
An n-dimentional analogue of a square is called an n-cube, or a hypercube. They can be constructed by numbering the vertices using n base-2 bits.
A 0-cube is just a point.
n = 1
A 1-cube is a line. Its vertices can be labeled using 1 bit.
n = 2
A 2-cube is a square. Its vertices can be labeled using 2 bits.
n = 3
A 3-cube is a cube. Its vertices can be labeled using 3 bits.
n = 4
A 4-cube is a tesseract. Its vertices can be labeled using 4 bits. This is where binary labeling of vertices can be especially useful, because it can help construct a tesseract.
In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2.
The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them which is equal to that prime. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.
The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes (below 10 million or so). It is named after Eratosthenes of Cyrene, a Greek mathematician; although none of his works have survived, the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus.
The sieve may be used to find primes in arithmetic progressions.
This is from Calculus Humor's wiki at http://calculushumor.wikia.com/wiki/Sieve_of_Eratosthenes!
Find the number of triangles. Assume the base is square.
Tell us your answers in the comments!
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