u/Charming-Detail-5247

Full Live Stream

The Gaussian integral is named after Carl Friedrich Gauss, whose work on the Gaussian (or normal) distribution made the function famous. The integral became an important result in the 19th century, revealing that a function with no elementary antiderivative can still be evaluated exactly over the entire real line. Today, it serves as a cornerstone of probability theory, statistics, physics, and mathematical analysis.

​

​

The Tollens' reagent test is a classic qualitative experiment used in organic chemistry to detect aldehydes. In the presence of an aldehyde, the silver ions in Tollens' reagent are reduced to metallic silver, producing a characteristic reflective coating known as the silver mirror reaction. This reaction serves as a clear demonstration of oxidation-reduction processes and remains one of the most recognizable tests in chemical analysis.

This animation demonstrates a classic visual proof for the area of a circle. The circle is divided into many thin sectors and rearranged alternately to form a shape that increasingly resembles a triangle or rectangle. In this arrangement, the base corresponds to the circle’s circumference while the height remains the radius , giving an area of . As the number of sectors increases, the approximation becomes mathematically exact through limits.

There are also other proofs for the same formula, including calculus-based integration, Archimedes’ geometric method, and proofs using infinitesimally thin concentric rings. One limitation of this visual proof is that with only a small number of sectors, the rearranged shape is not perfectly straight, so it’s more of an intuitive explanation until infinitely many slices are considered.

Sign this petition urgently regarding this matter

[Link](https://www.change.org/p/urgent-appeal-for-fair-re-evaluation-and-justice-in-cbse-class-12-board-results?recruiter=1411415377&recruited\_by\_id=b3ff90d0-4ac1-11f1-9bb5-b30a58f312c1&utm\_source=share\_petition&utm\_campaign=psf\_combo\_share\_initial&utm\_term=share\_petition&utm\_medium=copylink)

As transistor sizes continue shrinking with modern semiconductor fabrication (moving into a few nanometers and below), I’ve been wondering whether there is a hard physical limit to miniaturization.

At very small scales, quantum effects like electron tunneling start becoming significant, which could potentially cause leakage currents and unreliable switching in traditional CMOS transistors.

So my question is:

Is there a true “final limit” to how small we can make silicon-based transistors before they stop working effectively, or are advances in materials (like FinFETs, GAAFETs, or beyond-silicon technologies) expected to keep pushing this boundary further?

The Heisenberg Uncertainty Principle is a core rule of quantum mechanics that describes an unavoidable trade-off in what we can know about the microscopic world. It states that it is impossible to simultaneously measure both the exact position and the exact momentum (speed and direction) of a particle. The more precisely you pin down where a particle is, the less you can know about where it is going and how fast and vice versa.This is not due to clumsy measuring tools, but is a fundamental, built-in feature of the universe. Because particles also act like waves, their exact state is inherently “fuzzy,” meaning nature at its smallest scale is always governed by probability rather than strict certainty.

This video demonstrates the open siphon effect, where a liquid appears to pour itself out of a container without any tube. Unlike normal liquids, this fluid is viscoelastic, meaning it behaves both like a liquid and a stretchy solid, allowing it to form a continuous thread that doesn’t easily break. Once the flow starts, gravity pulls the liquid downward while its elasticity keeps the stream intact, letting it “pull” more fluid over the edge and sustain the flow through open air. The samples shown are a 0.5% solution of high molecular weight poly(ethylene oxide) (PEO) in water (red) and the same solution with added 45–60 nm silica nanoparticles (blue).

LEDs change color when submerged in Liquid Nitrogen. They produce light through Electroluminescence, where electrons recombine with holes and release energy as photons, and the color depends on the material’s Band Gap. At such low temperatures, the semiconductor’s band gap increases slightly, so the emitted photons have higher energy and shift toward shorter wavelengths causing visible color changes (for example, as seen here, yellow shifting toward green). Reduced thermal losses can also make the LED appear brighter and more efficient.

India’s hypersonic program is gaining momentum as the DRDO’s Long-Range Anti-Ship Missile (LR-AShM) moves into Phase-II trials. Designed as a hypersonic glide weapon capable of reaching speeds up to Mach 10 (around 12,300 km/h, or roughly 10 times the speed of sound), it can strike both moving and stationary targets while following a maneuverable trajectory that makes interception extremely difficult. The missile is part of a broader push toward a multi-layered strike capability, combining ballistic, cruise, and hypersonic systems for different combat roles. With indigenous sensors, advanced avionics, and enhanced naval strike potential, LR-AShM marks a major step in strengthening India’s deterrence and next-generation warfare capabilities.

Video Source: @NewsIADN

Microscopic footage of two Stentor-large, trumpet-shaped single-celled protozoans interacting in the same sample.Their flexible bodies can stretch and deform, sometimes creating the illusion of one passing through another. A fascinating glimpse into the dynamic world of microbial life.

Credit: @desi_morrison