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#motion

6 posts6 participants0 posts today
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Douglas E. Welch

The 4 Types of Luck by Sahil Bloom [Shared]

The 4 Types of Luck
In 1978, a neurologist named Dr. James Austin published a book entitled Chase, Chance, & Creativity: The Lucky Art of Novelty.

In it, Dr. Austin proposed that there are four types of luck:

Blind Luck
Luck from Motion
Luck from Awareness
Luck from Uniqueness
Here's how to think about each type:

welchwrite.com/blog/2025/04/15

The image features three white dice in mid-air against a dark background. The dice are captured in a dynamic state, with one die in the foreground showing a five, another in the middle showing a six, and the third in the background showing a five. The dice are illuminated by a light source from the upper left, casting shadows on the surface below. The focus is sharp on the dice, highlighting the black dots representing the numbers, while the background remains blurred, emphasizing the motion of the dice. The overall composition is minimalist, with the contrast between the white dice and the dark background creating a striking visual effect. Provided by @altbot, generated privately and locally using Ovis2-8B
#luck#think#Thinking
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Pustam | पुस्तम | পুস্তম🇳🇵

A cycloidal pendulum - one suspended from the cusp of an inverted cycloid - is isochronous, meaning its period is constant regardless of the amplitude of the swing. Please find the proof using energy methods: Lagrange's equations (in the images attached to the reply).

Background:
The standard pendulum period of \(2\pi\sqrt{L/g}\) or frequency \(\sqrt{g/L}\) holds only for small oscillations. The frequency becomes smaller as the amplitude grows. If you want to build a pendulum whose frequency is independent of the amplitude, you should hang it from the cusp of a cycloid of a certain size, as shown in the gif. As the string wraps partially around the cycloid, the effect decreases the length of the string in the air, increasing the frequency back up to a constant value.

In more detail:
A cycloid is the path taken by a point on the rim of a rolling wheel. The upside-down cycloid in the gif can be parameterized by \((x, y)=R(\theta-\sin\theta, -1+\cos\theta)\), where \(\theta=0\) corresponds to the cusp. Consider a pendulum of length \(L=4R\) hanging from the cusp, and let \(\alpha\) be the angle the string makes with the vertical, as shown (in the proof).

GIF
#Pendulum#Cycloid#Period
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