Atul Tripathi

Honorary Adjunct Fellow- National Maritime Foundation, Ex AI Consultant PMO (NSCS) #QuantumComputing
#AI #MachineLearning #Finance #ClimateRisk #DisasterRisk

[Mathematica @mathemetica]

Toroidal geometry places origin O at its center with major radius R to the tube axis and minor radius r setting the tube size.

Upper view marks these radii, angle α, and unit normal vector n_k hat. Central panel shows the gridded torus surface with red and blue winding curves near M1 and M2. Lower view projects the curves onto coordinates with x directed left, z up, y down.

It models closed field lines in toroidal magnetic confinement devices for fusion research.

[Interesting things @awkwardgoogle]

Your eyes are more advanced than any camera

[Math Files @Math_files]

In 1978, mathematician John McKay noticed something surprising: 196884 = 196883 + 1.

At first, this looks like a simple and meaningless coincidence. But it turned out to be something much deeper.

The number 196884 comes from a function in number theory called the j-invariant. The number 196883 comes from group theory, as part of the Monster group, a very large and complex mathematical object. At that time, these two areas of math were thought to be completely unrelated.

This small observation led to a big idea: maybe the numbers from the j-invariant are connected to the Monster group. This unexpected link between two different fields became known as “Monstrous Moonshine.”

After many years of work, this idea was finally proven in 1992 by Richard Borcherds.

[Mechanical Knowledge @mechanical_4u]

Globus - The Soviet Mechanical "Space GPS"

Before digital computers took over, Soviet spacecraft used something extraordinary: a fully mechanical navigation computer called Globus.

Installed in missions like Vostok and Soyuz, this device used a system of gears, cams, and rotating mechanisms to calculate the spacecraft's position in real time. As the capsule orbited Earth, Globus would continuously update-showing where the crew was above the planet.

No screens. No software.

Just pure engineering.

By factoring in orbital motion, Earth's rotation, and time, the system could accurately track ground position and even help determine reentry timing and landing zones.

It was reliable, self-contained, and didn't depend on external signals-making it perfect for the early space age.

A reminder that long before digital navigation... spaceflight was powered by clockwork precision.

[Mathematica @mathemetica]

The normal distribution features a symmetric bell curve centered at its mean μ, which matches the sample mean x̄, with spread indicated by σ.

The density function is f(x) = 1/(σ√(2π)) * e^(-(x-μ)²/(2σ²)), giving the relative likelihood at each x.
Its distribution function is F(x) = ∫_{-∞}^x [1/(σ√(2π)) * e^(-(t-μ)²/(2σ²))] dt.

It is used to calculate probabilities for continuous data like error margins in scientific measurements or heights in a population.

[yajnadevam @yajnadevam]

Curiously the quadratic formula is known in Brazil as Bhaskaras formula. Turns out the Portuguese started translating Indian texts from 1519 and took it to Europe and the new world. Over the next 200 years, all manner of mathematical, medical and philosophical concepts boom in Europe, which for some reason are also in Indian texts.

Interestingly multiple scholars invent the same science around the same time unknown to each other like Calculus.

[Parimal @Fintech03]

Nah... that is not even the best part. Here is the real FUN FACT:

In the Aryabhatiya (Ganitapada, Verse 21), written in 499 CE, Aryabhata introduces the mathematics of stacking. He explicitly lays out the formula for finding the total number of items in a pyramid pile with a triangular/square base. For a pyramid stack where each side of the base has 'n' spheres:

Total Spheres = [ n × (n + 1) × (n + 2) ] / 6

Think about the timeline here. Johannes Kepler conjectured that this layout was the densest in 1611. Aryabhata had already mapped out the exact algebraic discrete-volume matrix to count every single individual sphere within that dense packing formation 1000s yrs earlier.

Fun Fact is still not over. Fast-forward to the 12th century. The legendary mathematician Bhaskara II takes Aryabhata’s foundation & elevates it into a poetic, highly advanced art form in his textbook, the Lilavati. Bhaskara creates a dedicated mathematical category called Citi-Ghana (the volume of a pile). He did not just give 1 formula; he realized that different stacking bases create different geometric properties. He breaks down eqns for:

- Triangular-based pyramids (where spheres rest in the gaps of a triangular grid)
- Square-based pyramids (the standard grocery-stack style)
- Oblong piles (where the base is a rectangle)

To solve these, Bhaskara had to utilize Varga-Sankalita (the sum of squares of natural numbers) & Ghana-Sankalita (the sum of cubes). While Western mathematics at the time was struggling with basic arithmetic using Roman numerals, Indian scholars were utilizing advanced series expansions to handle the discrete boundaries of 3 dimensional sphere packing.

Now the Fun Fact is over 🙏🙏

[D Prasanth Nair @DPrasanthNair]

Many of us would not know him. Even many mathematicians would not realise his contribution.

His name : Kelallur Nilakantha Somayaji - a giant of the Kerala school of astronomy and mathematics. He was a disciple of Damodara, who was himself the son and student of the school's legendary founder, Madhava of Sangamagrama.

1. ​Long before Nicolaus Copernicus published his heliocentric theory in Europe, Nilakantha mathematically formulated a remarkably similar quasi-heliocentric model in his landmark 1501 treatise, the Tantrasangraha.
2. In his comprehensive commentary on the Aryabhatiya, Nilakantha explicitly stated that pi is an irrational number.
3. Grahapariksakrama is his another work which is a manual on making observations in astronomy based on instruments of the time.

Let us celebrate the ancient contribution of India in science and mathematics

[Dr. Khulood Almani | د.خلود المانع @Khulood_Almani]

🚨 🤖🧠 What are the 7️⃣ #skills #AI can’t replace in 2026 & 2027❓

💡 As AI scales speed & automation, these human capabilities remain non-automatable & mission-critical.

Here’s what still requires humans ⤵️

1️⃣ Emotional Intelligence ❤️
↳ Reading nuance, intent & what’s left unsaid
↳ Leading people, not just systems
⚠️ Trust cannot be automated

2️⃣ Strategic Vision 🔭
↳ Seeing around corners before the data is obvious
↳ Defining direction under uncertainty
⚠️ AI predicts but leaders decide

3️⃣ Ethical Judgment ⚖️
↳ Making decisions in gray zones where rules fall short
↳ Owning responsibility & consequences
⚠️ Accountability is human

4️⃣ Creative Problem-Solving 🎨
↳ Reframing problems beyond existing data
↳ Creating paths where no precedent exists
⚠️ Optimization ≠ invention

5️⃣ Relationship Building 🤝
↳ Building long-term trust, influence & credibility
↳ Navigating emotions and power dynamics
⚠️ Networks are not relationships

6️⃣ Cultural Intelligence 🌍
↳ Understanding context across cultures & values
↳ Reducing bias through awareness, not just filters
⚠️ Context can’t be fully encoded

7️⃣ Adaptive Learning 🔄
↳ Turning experience and failure into judgment
↳ Evolving wisdom over time
⚠️ Learning ≠ retraining

🎯Bottom line:
AI scales execution.
Humans define meaning, direction and impact.

by/ Daniel Hartweg

#Leadership #FutureOfWork #HumanSkills

@enilev @Jagersbergknut @TysonLester @CurieuxExplorer @GlenGilmore @chidambara09 @jeancayeux @mvollmer1 @Nicochan33 @RLDI_Lamy @pchamard @mikeflache @FrRonconi @Fabriziobustama @Mack1510019 @PawlowskiMario @theomitsa @drsharwood @kalydeoo @baski_LA @AnthonyRochand @smaksked @Eli_Krumova @andresvilarino @gvalan @bimedotcom @arlenenewbigg @NewsNeus @domingonarvaez1 @jornalistavitor @jblefevre60 @thomas_dettling @FmFrancoise @nafisalam @Mhcommunicate @Corix_JC @c4trends @ipfconline1 @smoothsale @amalmerzouk @PVynckier @bbailey39 @SiddharthKS @NathaliaLeHen @jasuja @ralf_ladner @c4trends @SabineVdL @mary_gambara

[Mathematica @mathemetica]

Trifolium Rose Curve via Parametric Gear Coupling

Gear ratio 3:1.
A fixed point on the linkage traces a perfect periodic path in the rotating frame of the larger gear.

Orthogonal projections (blue) physically realize:
r = a cos(3θ)

[Kiren Rijiju @KirenRijiju]

Learn from Mizoram, our North East !
जिस किसी ने भी यह वीडियो बनाया है, मैं उससे सहमत हूँ।

[The Math Flow @TheMathFlow]

The Stunning Geometry of Higher-Order Exponents.

[Engineer Things @EngineerThing]

How Electric Iron Works ⚡

[Massimo @Rainmaker1973]

Points of view

[TheNewPhysics @CharlesMullins2]

🚨 SCIENTISTS JUST CREATED MATTER FROM PURE LIGHT.

For the first time in laboratory history, researchers smashed high-energy photons together and directly produced matter and antimatter particles.

No atoms.
No pre-existing matter.

Just light turning into mass.
It’s called the Breit–Wheeler process a phenomenon predicted in 1934…
…but never directly observed in a controlled experiment until now.

Einstein was right all along:
E = mc²
Energy and matter are fundamentally interchangeable.
And now scientists have literally watched light transform into particles.

The experiment used ultra-powerful lasers to collide photons with enough energy to create:
• electrons
• positrons
• bursts of pure matter-antimatter pairs

The deeper implication is staggering:
The solid universe around you may ultimately be condensed energy structures frozen into stable form.

Matter may not be the “base layer” of reality at all.
Light came first.
And under extreme conditions… reality can crystallize directly out of energy itself.

This also mirrors conditions believed to exist moments after the Big Bang when the early universe was so energetic that matter continuously formed from radiation.

We are now recreating pieces of the birth of the universe inside a laboratory.
What happens when humans learn to engineer matter directly from energy at scale?

Follow for more frontier physics and reality-bending discoveries.

[Knowledge & History @xKnowledgeBANK]

Visualization of the Moon's gravitational Influence on Earth. This is how tides are formed.

[Massimo @Rainmaker1973]

Small objects can show that gravity is real.

The Cavendish experiment proved that even tiny masses pull on each other, showing gravity works everywhere, not just between planets.

[Science Simplified @Scivf4]

Double slit interference

[Mathelirium @mathelirium]

General Relativity allows a geometry where two distant regions of Spacetime become connected through a curved throat.

In 1935, Albert Einstein and Nathan Rosen showed that the Schwarzschild solution can be extended into a bridge-like structure. The metric is

ds² = −(1 − 2M/r)dt² + (1 − 2M/r)⁻¹dr² + r²dΩ²

Under maximal coordinate extension, the Spacetime splits into two asymptotically flat regions joined through a narrow throat called, the Einstein–Rosen bridge.

It's a geometric structure emerging directly from Einstein’s field equations.

#EinsteinRosenBridge #GeneralRelativity #SpacetimeGeometry #BlackHolePhysics #EinsteinFieldEquations #Relativity