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Every triangle hides an equilateral triangle, even when the original triangle is completely irregular. Take any triangle. Divide each of its three angles into three equal parts. Now consider the intersections of the adjacent internal angle trisectors. The three intersection points always form an equilateral triangle. No condition is... show more

Math Files

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15,259 views • 8 days ago •via X (Twitter)

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9 Comments

Razvan Caraghin7 days ago

A sign there's a deeper connection there to other math fields and physics 😎

Raúl Blanco7 days ago

Esa no me la sabía Gracias

Darryl T7 days ago

Shame there’s no geometric process to trisect an angle like there is to bisect an angle.

Annette Schaper-Herget8 days ago

Would you please provide a link to the proof? Thanks

ilario della noce8 days ago

And the biggest (inside) is built in an equilateral triangle, (assuming constant area ?).

sofie n ✿7 days ago

triangle said ok but the trisectors were not consulted

我不会说中文 🆗7 days ago

It doesn't seem that special because you start by dividing the angles in to 3 equal parts. Equality in, equality out.

mathingsense7 days ago

.

TheGradient7 days ago

사영기하학적 및 아핀 변환의 관점 평면 위에 놓인 임의의 비대칭 삼각형이 있을 때, 3차원 공간에서 이를 적절한 각도로 기울이거나 평행 투영(Parallel Projection)을 수행하면 항상 정삼각형으로 투영할 수 있다. 정삼각형은 안에 하나, 밖에 하나 있다.

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Where is the triangle? Alex O'Connor thinks consciousness is the one thing materialism can't explain away and he has a deceptively simple argument for it. Close your eyes. Picture a triangle. You can see it. The shape, the angles, maybe even the colour. It's right there, vivid and undeniable. Now ask yourself: where is that triangle? According to Alex, this single question cuts to the heart of one of philosophy's oldest problems. A strict materialist, someone who believes everything in the universe reduces to physical matter has to say that triangle exists somewhere in the neurons of your brain. But if a neurosurgeon cracked open your skull right now, they wouldn't find a triangle anywhere inside. "If everything you experience is reducible to the material when I close my eyes and see a triangle, there really is a triangle there. I can see it. It's there. And I think well, where is that triangle? The materialist has to say it's reducible to just somewhere in your brain. But if I cut open your brain I'm not going to find a triangle inside of it." He anticipates the obvious pushback. When he raised this on YouTube, commenters pointed to computers as a counter-example: if you cut open a computer, you won't find the triangle it's displaying on screen either. But the hardware is still producing a real image on a real screen. Alex's response is that this analogy doesn't hold because the mind has no screen. There is no separate interface between the brain's processing and the experience of seeing. The brain is the computer and the screen. Which only deepens the mystery: somehow, purely physical processes are generating a first-person, subjective experience: colours, shapes and images that can't be located anywhere in physical space. "It's as if the computer itself somehow had a triangle in the computer's own first-person subjective experience. Like where is that triangle that you can picture in your head? Where the hell is it?" For Alex, consciousness isn't just another interesting puzzle in the philosophy of mind. It's the big objection to materialism. The thing that, once you sit with it, seems to demand that there is something more going on than matter arranged in clever ways. He points to something as ordinary as dreaming as a case in point. Every night you produce vivid images full scenes, faces, colours without any external input. An entire visual world conjured from nowhere. Where does it come from? Where does it go? "Even just when you have an average dream, it's fascinating to think what's going on there. You've got images in your head, you can close your eyes and you can picture things, you can see colours, you can see shapes in your head. Like where are those shapes?" The triangle thought experiment has a way of making this undeniable. It's not abstract. You can do it right now. And when you do, you run headfirst into the hard problem of consciousness: the gap between the physical description of the brain and the felt quality of experience that no amount of neuroscience has yet bridged. Whether you find Alex's argument convincing or not, the question it raises is genuine: how does purely physical matter give rise to the inner world we each inhabit a world of colours, shapes, memories, and dreams that exists nowhere except in the first person?

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Aralez 🐕

76,117 views • 4 months ago

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71,821 views • 4 months ago

🚨 COVID HISTORY IS ABOUT TO REPEAT... Look at this yourself: COVID-19 ( 2020-2021 ): Starting from 2018, market began forming an “Expanding Triangle” pattern built around 6 stages Stage #5 - market top, pure EUPHORIA before the global crisis Stage #6 - local bottom, a -36% collapse in just 2 weeks... HANTAVIRUS ( 2026-???? ): Now index is forming the exact same “Expanding Triangle” pattern - again in 6 stages Price is currently sitting at Stage #5 - market just printed a new ATH, while euphoria and belief in “endless growth” are spreading across investors Next comes Stage #6 - implying a potential 30%+ drop, with 4,600-4,800 zone acting as first downside target This pattern warned about one of the biggest crashes before and now history may be repeating once again... When market is literally “screaming” about an incoming collapse - I sell assets Don’t make a massive mistake - turn on notifs, I’ll update

🚨 COVID HISTORY IS ABOUT TO REPEAT... Look at this yourself: COVID-19 ( 2020-2021 ): Starting from 2018, market began forming an “Expanding Triangle” pattern built around 6 stages Stage #5 - market top, pure EUPHORIA before the global crisis Stage #6 - local bottom, a -36% collapse in just 2 weeks... HANTAVIRUS ( 2026-???? ): Now index is forming the exact same “Expanding Triangle” pattern - again in 6 stages Price is currently sitting at Stage #5 - market just printed a new ATH, while euphoria and belief in “endless growth” are spreading across investors Next comes Stage #6 - implying a potential 30%+ drop, with 4,600-4,800 zone acting as first downside target This pattern warned about one of the biggest crashes before and now history may be repeating once again... When market is literally “screaming” about an incoming collapse - I sell assets Don’t make a massive mistake - turn on notifs, I’ll update

Aralez 🐕

55,109 views • 5 months ago

"A Drone Reached The Bottom of The Bermuda Triangle, What It Filmed Shocked Everyone" What if I told you that a drone descended to the bottom of the Bermuda Triangle last summer, and what it filmed in the final 11 minutes of its descent has been classified, suppressed, and quietly leaked to a handful of researchers who refuse to be named publicly? Not a few hours of routine seafloor video. Not a flat sediment plain. Something else entirely. For 80 years, the Bermuda Triangle has swallowed ships, aircraft, and human beings without leaving a trace. Five Navy bombers vanished mid-flight on a routine training run. A 542-foot supply ship disappeared with 306 men aboard. Commercial airliners blinked off radar in cloudless skies. And for eight decades, no one could get close enough to the bottom to find out what had happened to them. The pressure was too extreme. The trenches were too deep. The technology didn't exist. Until last year. In July 2024, an autonomous deep-sea drone reached the floor of the Brownson Deep, the lowest point of the entire Atlantic Ocean, and its cameras captured three things at the same time. The first was a graveyard of ships so vast that the team aboard the surface vessel lost the ability to count them in real time. The second was a series of geometric formations on the seafloor that, in the lead researcher's own words, are "inconsistent with any known geological process at that depth." The third was something moving along the edge of those formations for less than four seconds before the drone's signal severed instantly and the vehicle was lost forever. What that footage shows, and what the scientists who've reviewed it are now saying behind closed doors, doesn't just explain 80 years of missing ships. It rewrites the entire history of the Atlantic floor.

"A Drone Reached The Bottom of The Bermuda Triangle, What It Filmed Shocked Everyone" What if I told you that a drone descended to the bottom of the Bermuda Triangle last summer, and what it filmed in the final 11 minutes of its descent has been classified, suppressed, and quietly leaked to a handful of researchers who refuse to be named publicly? Not a few hours of routine seafloor video. Not a flat sediment plain. Something else entirely. For 80 years, the Bermuda Triangle has swallowed ships, aircraft, and human beings without leaving a trace. Five Navy bombers vanished mid-flight on a routine training run. A 542-foot supply ship disappeared with 306 men aboard. Commercial airliners blinked off radar in cloudless skies. And for eight decades, no one could get close enough to the bottom to find out what had happened to them. The pressure was too extreme. The trenches were too deep. The technology didn't exist. Until last year. In July 2024, an autonomous deep-sea drone reached the floor of the Brownson Deep, the lowest point of the entire Atlantic Ocean, and its cameras captured three things at the same time. The first was a graveyard of ships so vast that the team aboard the surface vessel lost the ability to count them in real time. The second was a series of geometric formations on the seafloor that, in the lead researcher's own words, are "inconsistent with any known geological process at that depth." The third was something moving along the edge of those formations for less than four seconds before the drone's signal severed instantly and the vehicle was lost forever. What that footage shows, and what the scientists who've reviewed it are now saying behind closed doors, doesn't just explain 80 years of missing ships. It rewrites the entire history of the Atlantic floor.

Jordan Chain

1,075,070 views • 4 months ago

I imported 7 of Jonas’ photos into Agisoft Metashape, where I used its photogrammetric triangulation feature to match key points across the photos. By calculating corresponding points in multiple images, the software determined the camera’s orientation and position in three-dimensional space for each photo. The resulting positions, angles, and distances match what would be expected from a camera on a plane and match the specific details of Jonas’ photos, e.g., zoom, angle, and time between photos. This further proves that the Jonas photos are real, naturally taken photos that have not been manipulated. Their use in the MH370 “satellite” video is extremely strong evidence that the “satellite” video is fake. #MH370x

I imported 7 of Jonas’ photos into Agisoft Metashape, where I used its photogrammetric triangulation feature to match key points across the photos. By calculating corresponding points in multiple images, the software determined the camera’s orientation and position in three-dimensional space for each photo. The resulting positions, angles, and distances match what would be expected from a camera on a plane and match the specific details of Jonas’ photos, e.g., zoom, angle, and time between photos. This further proves that the Jonas photos are real, naturally taken photos that have not been manipulated. Their use in the MH370 “satellite” video is extremely strong evidence that the “satellite” video is fake. #MH370x

Tony Adams

77,342 views • 1 year ago

It (the US) has devastated Iran's military capability, its ability to make nuclear weapons, and its ability to produce missiles. It has eroded Iran's ability to spread terrorism. There is a little more to be done over the next two to three weeks, and Trump is keeping his commitment that this will not become an endless war.- Fred Fleitz Trump’s speech was 100 percent designed for a domestic audience—his base. Once again, it shows that there was no clear objective at the beginning of the war, and it may end without any defined objective.- Patrick N. Theros #NewsToday Rajdeep Sardesai

It (the US) has devastated Iran's military capability, its ability to make nuclear weapons, and its ability to produce missiles. It has eroded Iran's ability to spread terrorism. There is a little more to be done over the next two to three weeks, and Trump is keeping his commitment that this will not become an endless war.- Fred Fleitz Trump’s speech was 100 percent designed for a domestic audience—his base. Once again, it shows that there was no clear objective at the beginning of the war, and it may end without any defined objective.- Patrick N. Theros #NewsToday Rajdeep Sardesai

IndiaToday

30,247 views • 6 months ago

CHINA WEAPONIZES THE STRAIT OF HORMUZ: THE 1.4 BILLION BARREL DEMAND STRIKE SET TO CRUSH OIL PRICES Troy W. Eckard of Eckard Enterprises has spent 41 years inside the oil and gas industry. He now reveals how the Strait of Hormuz has become a Bermuda Triangle of daily uncertainty and how China is weaponizing that chaos from the demand side in a way never seen before. What he describes next explains why oil prices may behave so differently in the months ahead. THE BERMUDA TRIANGLE OPENS THE DOOR ➡️ The Strait of Hormuz now operates like the Bermuda Triangle where vessels and 20,000 mariners never know from one day to the next whether safe passage exists. ➡️ This constant uncertainty created the perfect opening for a new kind of energy power play. THE CHINA DEMAND WEAPON ➡️ For the last 45 days China stopped buying 6 to 7 million barrels per day in the open market. ➡️ Instead Beijing is draining its 1.4 billion barrel strategic reserves to create intentional demand destruction. ➡️ Eckard states clearly this is worse than normal demand destruction because it is completely intentional and calculated. ➡️ The result could push oil prices into the low 70s, the 60s, or even the $50 range. THE PRODUCER SQUEEZE ➡️ Crushed prices force companies worldwide to slash capital spending and delay new drilling projects. ➡️ China simply waits to refill its own storage at the lowest prices once producers capitulate. ➡️ This demand swing tactic has never appeared in Eckard’s four decade career. THE 180 DAY POWER PLAY ➡️ China consumes 11.5 to 11.7 million barrels daily yet produces only 4.5 million barrels at home. ➡️ Its reserves give Beijing the ability to halt all imports for roughly 180 days if required. ➡️ No supply swing player has ever held this level of demand side leverage until now. THE BOTTOM LINE China has turned Strait of Hormuz uncertainty into a powerful demand weapon that lets them crush prices today and quietly restock tomorrow at everyone else’s expense. This is the sound of a new energy order being born where demand manipulation becomes the ultimate strategic tool. HT: YouTube Eckard Enterprises | Oil & Gas Investing #ChinaOilWeapon #HormuzBermudaTriangle #IntentionalDemandDestruction #OilPriceManipulation #EnergyGeopolitics #StraitOfHormuz #ChinaReserves

CHINA WEAPONIZES THE STRAIT OF HORMUZ: THE 1.4 BILLION BARREL DEMAND STRIKE SET TO CRUSH OIL PRICES Troy W. Eckard of Eckard Enterprises has spent 41 years inside the oil and gas industry. He now reveals how the Strait of Hormuz has become a Bermuda Triangle of daily uncertainty and how China is weaponizing that chaos from the demand side in a way never seen before. What he describes next explains why oil prices may behave so differently in the months ahead. THE BERMUDA TRIANGLE OPENS THE DOOR ➡️ The Strait of Hormuz now operates like the Bermuda Triangle where vessels and 20,000 mariners never know from one day to the next whether safe passage exists. ➡️ This constant uncertainty created the perfect opening for a new kind of energy power play. THE CHINA DEMAND WEAPON ➡️ For the last 45 days China stopped buying 6 to 7 million barrels per day in the open market. ➡️ Instead Beijing is draining its 1.4 billion barrel strategic reserves to create intentional demand destruction. ➡️ Eckard states clearly this is worse than normal demand destruction because it is completely intentional and calculated. ➡️ The result could push oil prices into the low 70s, the 60s, or even the $50 range. THE PRODUCER SQUEEZE ➡️ Crushed prices force companies worldwide to slash capital spending and delay new drilling projects. ➡️ China simply waits to refill its own storage at the lowest prices once producers capitulate. ➡️ This demand swing tactic has never appeared in Eckard’s four decade career. THE 180 DAY POWER PLAY ➡️ China consumes 11.5 to 11.7 million barrels daily yet produces only 4.5 million barrels at home. ➡️ Its reserves give Beijing the ability to halt all imports for roughly 180 days if required. ➡️ No supply swing player has ever held this level of demand side leverage until now. THE BOTTOM LINE China has turned Strait of Hormuz uncertainty into a powerful demand weapon that lets them crush prices today and quietly restock tomorrow at everyone else’s expense. This is the sound of a new energy order being born where demand manipulation becomes the ultimate strategic tool. HT: YouTube Eckard Enterprises | Oil & Gas Investing #ChinaOilWeapon #HormuzBermudaTriangle #IntentionalDemandDestruction #OilPriceManipulation #EnergyGeopolitics #StraitOfHormuz #ChinaReserves

Mark

47,024 views • 3 months ago