# What is this equation called and why is it regarded as beautiful?

• B
• Physics Slayer
In summary, the equation being discussed is the fundamental theorem of calculus, also known as the generalized Stokes' theorem. It states that to understand what is happening within a region, it is enough to know what is happening on its boundary. This concept was discovered by mathematician James Gregory in 1667, long before it was recognized by physicist Leonard Susskind in 1997. However, the equation may lose its beauty when considering all the additional conditions and definitions attached to it. For more information, one can refer to Robert Ghrist's CalcBLUE 4, specifically chapters 18.1-18.5.
Physics Slayer
$$\int_S dw = \int_{dS}w$$
Saw a few seniors talking about this equation, I don't know what it is called hence I can't google it, It doesn't look very correct as the RHS integral doesn't have a differential and both the limits look incomplete.
(they looked like they knew what they were talking about)

where can I study this equation and see its beauty?

also it didn't show up when searching for the most elegant/beautiful math equations, so maybe it isn't that significant?

ohwilleke and Hamiltonian
It is the fundamental theorem of calculus: In order to know what is going on inside a region, it is sufficient to know what's going on at the boundary.

Personal remark: It Seems mathematicians found the holographic principle 328 years prior to physicists (James Gregory 1667 vs. Leonard Susskind 1997), .

ohwilleke, Klystron and Physics Slayer
FWIW, it is less beautiful once you add all the terms, conditions and definitions to it in fine print (smoothness, continuity, domain of permissible values, etc.), like a great sale on a new car with a half a page of fine print attached.

Physics Slayer
ohwilleke and Physics Slayer

## 1. What is this equation called?

This equation is called the Golden Ratio, also known as the Divine Proportion or the Golden Mean.

## 2. Why is it regarded as beautiful?

The Golden Ratio is regarded as beautiful because it has been observed in nature and art for centuries, and is believed to create aesthetically pleasing proportions. It is also considered to be a fundamental mathematical constant that represents balance and harmony.

## 3. Can you explain the equation?

The Golden Ratio is a mathematical ratio of approximately 1.618, represented by the Greek letter phi (φ). It is derived by dividing a line into two parts so that the ratio of the longer part to the shorter part is equal to the ratio of the sum of both parts to the longer part.

## 4. How is the Golden Ratio used?

The Golden Ratio has been used in various fields such as art, architecture, design, and even in the stock market. It is believed to create visually appealing compositions and is often used as a design principle in these fields.

## 5. Is the Golden Ratio considered to be a universal constant?

While the exact value of the Golden Ratio may vary depending on the context, it is considered to be a universal constant as it is found in many natural and man-made structures, suggesting that it is a fundamental aspect of the universe.

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