Dec 15, 2023
4D Gamer Girl (Hyperplane)
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4D Gamer Girl (Hyperplane)
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Equation of a hyperplane, and shortest distance between two hyperplanes.
[Click here for a PDF version of this post] Scalar equation for a hyperplane. In our last post, we found, in a round about way, that Theorem 1.1: The equation of a \(\mathbb{R}^N\) hyperplane, with distance \( d \) from the origin, and normal \( \mathbf{\hat{n}} \) is \begin{equation*} \Bx \cdot \mathbf{\hat{n}} = d. \end{equation*} Start proof: Let \( \beta = \setlr{ \mathbf{\hat{f}}_1, \cdots…
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Cryona's New Look (Hyperplane)
[Hyperplane.]
ECE1505H Convex Optimization. Lecture 4: Sets and convexity. Taught by Prof. Stark Draper
ECE1505H Convex Optimization. Lecture 4: Sets and convexity. Taught by Prof. Stark Draper
ECE1505H Convex Optimization. Lecture 4: Sets and convexity. Taught by Prof. Stark Draper
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Disclaimer
Peeter’s lecture notes from class. These may be incoherent and rough.
These are notes for the UofT course ECE1505H, Convex Optimization, taught by Prof. Stark Draper, covering [1] content.
Today
more on various sets: hyperplanes,…
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The present (or now) is the time range associated with the events perceived directly for the first time, not as a recollection (perceived more than once) or a speculation (predicted, hypothesis, uncertain). It is a period of time between the past and the future, and can vary in meaning from an instant to a day or longer. It is sometimes represented as a hyperplane in space-time, typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely for observers in relative motion.
Wikipedia
Rough draft of Song1 (proposed lyrics)
restx2
I blocked your number now And I unfollowed you And I deleted messages And I'm done with you now I ate an acid brick And I'm not even feeling sick And you can suck my dick 'Cause I'm feeling great now-aaahhhhh
restx2
The world is opening before- me And I wish you were here to see- restx4
Now I'll, destroy, what you've become
And I'm, no long, -er feeling numb
The time, has come, to come undone
And your, no long, -er number one
I blocked your number now And I unfollowed you And I deleted messages And I'm done with you now I ate an acid brick And I'm not even feeling sick And you can suck my dick 'Cause I'm feeling great now-aaahhhhh
Ham sandwich theorem
The Ham sandwich theorem (or the Stone-Tukey theorem) states that n measurable objects in n-dimensional space can be divided in half by one single ((n-1)-dimensional) hyperplane.
In three dimensions the popular interpretation is that a sandwich with three layers (say, bread, ham and cheese) can be cut in two pieces which contain the same amount of bread, ham and cheese.
In two dimensions, two flat pancakes of any form can be divided in half with one single cut.
(Image found here)