First Sub^5-topic
I am a formula and live here.
\[ e^{i\pi} +1 = 0 \]
You will need to prove this identity at the exam.
Additionally you'll be asked the following definitions:
Manhattan Metric: Let \(p=(p_1,p_2,...,p_n) \in \mathbb{R}^n\) and \(q=(q_1,q_2,...,q_n) \in \mathbb{R}^n\). The Manhattan- or Taxicab-Metric \(d_1\) is defined by:
\[ d_1(p,q):=\sum_{i=1}^n|p_i-q_i|\]
Neighbourhood: Let \(N = (x_1, x_2, . . . , x_n)\) be a vector of \(n\) distinct elements of \(\mathbb{Z}^d\) . Then the neighbours of a cell at location \(x \in \mathbb{Z}^d\) are the \(n\) cells at locations \(x + x_i\) for \(i = 1, 2, . . . , n.\)
Chebyshev-Metric: Let \(p=(p_1,p_2,...,p_n) \in \mathbb{R}^n\) and \(q=(q_1,q_2,...,q_n) \in \mathbb{R}^n\). The Chebyshev-Metric \(d_{Chebyshev}\) is defined by:
\[ d_{Chebyshev}(p,q):=\max_i(|p_i - q_i|)\]
Moore-Neighbourhood: Let \(p \in \mathbb{Z}^d.\) The Moore-Neighbourhood of range \(r\) of \(p\) is \(p\) itself and all cells \(q_i\) for which
\[ d_{Chebyshev}(p,q_i)\le r\]
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