# Questions tagged [experimental-mathematics]

The utilization of advanced computing technology in mathematical research: new mathematical results discovered partly or entirely with the aid of computer-based tools.

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### How can I create a characteristic curve from several 2D point clouds?

I study mechanical engineering and I want to create a characteristic of a hydraulic component. A hydraulic component has a correlation between speed and force. I measure distance, force and time and ...
1 vote
59 views

### Probability distribution for the perimeter of a random triangle in a circle

This is the same question as this question except that the random triangles do not need to necessarily touch the circle and I am only interested in the distribution for the perimeter. And I am ...
62 views

### Probability of All Decimal Digits Appearing in a Ten-Digit-Block of Pi Assuming Normality

In their book A Biography of the World's Most Mysterious Number, Posamentier and Lehmann mentioned that "Conway has indicated that if you separate the decimal value of $\pi$ into groups of ten ...
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### Bifurcation in accumulation points of sequence

I stumbled upon what seems like an interesting bifurcation. I wonder if anyone has an explanation for this. Here are the details: Let $a_n\in\mathbb{R}$, $n \in \mathbb{N}$ be a sequence. Define a new ...
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### Curve Fitting and Parameter Estimation Study

I have a problem with an experimental data analysis to obtain unknown parameters. The experimental data can be described by the equation: $y_k-y_{k-1}=\eta_k (x_k^{1-\alpha_k}-x_{k-1}^{1-\alpha_k})$ ...
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### On the elliptic curve $u(u+2186^2)(u+2188^2)=v^2$ and 7th powers?

I. Elliptic curve Given some constant integer $m$, a solution to the elliptic curve, $$E:=u\big(u+(m^7−1)^2\big)\big(u+(m^7+1)^2\big)=v^2$$ which is not a torsion point implies a polynomial identity ...
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### What is correlation dimension, actually?

I'm taking a course on chaotic dynamical systems, and we're talking about attractors with non-integer correlation dimensions, but I can't seem to find a satisfactory definition for this concept. ...
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1 vote
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### Asymptotic for $\sum_{k=1}^n k^n$

Consider the OEIS sequence A031971, which is defined as: $$a_n=\sum\limits_{k=1}^n k^n\quad\color{gray}{(1,\,5,\,36,\,354,\,4425,\,67171,\,1200304,\,.\!.\!.\!)}\tag{1}$$ I'm interested in the ...
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### When to use Pooled Variance?

In the following examples, why is pooled variance used in the first video but not in the other? When do you use pooled variance? https://classroom.udacity.com/courses/ud257/lessons/4018018619/...
1 vote
63 views

### Is division purely an arithmetic operator? Is it not the combination of arithmetic operation and relational operation?

An algorithm for computing the ratio of two positive numbers is the following: determine the number of times that the divisor can be subtracted from the numerator, until the accumulated effect of the ...
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### How many times should I perform an experiment to get a high level of accuracy?

I have an experiment with 4 factors (independent variables). The first and second variable have 8 levels, the third 5 and the fourth only 3 levels. Theres one dependent variable. How many times should ...
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### The closed-form solution of the family $\sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{1}{nm(pn+m)}$?
(The results below extend this post.) Given the Clausen function $\operatorname{Cl}_n\left(z\right)$. And, \begin{aligned} \operatorname{Cl}_2\left(\frac\pi2\right) &= \text{Catalan's constant}\...