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A mathematical construction in which one strip completes exactly ten turns. The polar angle of the generating curve is controlled by the exponential φ(θ) = (π/2) e^{-θ/8π}. Successive windings therefore nest inside one another, forming a compact layered rose with an exponentially tapering profile.

Matheorems

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Euler's formula states that e^(iθ) = cos θ + i sin θ. As the angle θ increases, e^(iθ) traces the unit circle in the complex plane. Plotted against θ, that rotation becomes a helix. The real part of the helix projects as the cosine wave Re(z) = cos θ. The imaginary part projects as the sine wave Im(z) = sin θ.

Euler's formula states that e^(iθ) = cos θ + i sin θ. As the angle θ increases, e^(iθ) traces the unit circle in the complex plane. Plotted against θ, that rotation becomes a helix. The real part of the helix projects as the cosine wave Re(z) = cos θ. The imaginary part projects as the sine wave Im(z) = sin θ.

Matheorems

55,150 Aufrufe • vor 14 Tagen

A bar magnet spinning at angular speed Ω is a magnetic dipole m turning in its own plane, and it radiates at f = Ω/2π. In that plane E points straight out of it, E ∝ m̈ × r̂ at the retarded time t − r/c, so each far crest lies on θ = φ(t − r/c) + π/2: two spiral arms of pitch λ = 2πc/Ω. The whine is 1024f, ten octaves up. In empty space J = 0, so in ∇ × B = μ₀ε₀ ∂E/∂t + μ₀J only the changing E keeps B alive. The radiated power grows as Ω⁴.

A bar magnet spinning at angular speed Ω is a magnetic dipole m turning in its own plane, and it radiates at f = Ω/2π. In that plane E points straight out of it, E ∝ m̈ × r̂ at the retarded time t − r/c, so each far crest lies on θ = φ(t − r/c) + π/2: two spiral arms of pitch λ = 2πc/Ω. The whine is 1024f, ten octaves up. In empty space J = 0, so in ∇ × B = μ₀ε₀ ∂E/∂t + μ₀J only the changing E keeps B alive. The radiated power grows as Ω⁴.

matharium

23,468 Aufrufe • vor 6 Tagen

A rose curve is r = sin(kθ). Here k = b/a, with a = 1, 3, 7 down the rows and b = 2, 4, 8 across. With k = p/q in lowest terms and pq even, the rose has 2p petals and closes after θ = 2qπ. Each a is odd and each b a power of 2, so p = b and q = a: each column has 2b petals, 4, 8 and 16, and a only sets how far they wind: 2π, 6π, 14π. Swept over θ ∈ [0, 2aπ] in equal times, kθ = 2πb·t/T, so a column's three pens reach their petal tips together.

A rose curve is r = sin(kθ). Here k = b/a, with a = 1, 3, 7 down the rows and b = 2, 4, 8 across. With k = p/q in lowest terms and pq even, the rose has 2p petals and closes after θ = 2qπ. Each a is odd and each b a power of 2, so p = b and q = a: each column has 2b petals, 4, 8 and 16, and a only sets how far they wind: 2π, 6π, 14π. Swept over θ ∈ [0, 2aπ] in equal times, kθ = 2πb·t/T, so a column's three pens reach their petal tips together.

matharium

11,401 Aufrufe • vor 8 Tagen

3D rotation matrices about coordinate axes. Rₓ(θ) fixes x and rotates yz-plane [[1 0 0] [0 cosθ −sinθ] [0 sinθ cosθ]]. Rᵧ(θ) fixes y and rotates xz-plane [[cosθ 0 sinθ] [0 1 0] [−sinθ 0 cosθ]]. Rz(θ) fixes z and rotates xy-plane [[cosθ −sinθ 0] [sinθ cosθ 0] [0 0 1]].

3D rotation matrices about coordinate axes. Rₓ(θ) fixes x and rotates yz-plane [[1 0 0] [0 cosθ −sinθ] [0 sinθ cosθ]]. Rᵧ(θ) fixes y and rotates xz-plane [[cosθ 0 sinθ] [0 1 0] [−sinθ 0 cosθ]]. Rz(θ) fixes z and rotates xy-plane [[cosθ −sinθ 0] [sinθ cosθ 0] [0 0 1]].

Matheorems

16,127 Aufrufe • vor 10 Tagen

YEMEN UAP Three pieces of “debris” (identical IR signatures) appear to emerge from the object *in succession.* That is inconsistent with a kinetic strike ripping debris off of an object. It’s almost like they were inside the UAP and emerged one-by-one.

YEMEN UAP Three pieces of “debris” (identical IR signatures) appear to emerge from the object in succession. That is inconsistent with a kinetic strike ripping debris off of an object. It’s almost like they were inside the UAP and emerged one-by-one.

Marik vR

601,240 Aufrufe • vor 1 Jahr

Another angle of the near train collision of a school bus in Sumter County, Florida has been posted Earlier footage from inside the school bus showed the kids yelling as they almost got hit Sumter County Sheriff's Office said Yvonne Hampton is accused of 29 counts of child neglect and one count of endangering an adult

Another angle of the near train collision of a school bus in Sumter County, Florida has been posted Earlier footage from inside the school bus showed the kids yelling as they almost got hit Sumter County Sheriff's Office said Yvonne Hampton is accused of 29 counts of child neglect and one count of endangering an adult

Wall Street Apes

17,791 Aufrufe • vor 5 Monaten

#BREAKING Two vehicles have been swept away by fast-moving floodwaters in Oxford. The rear tail lights of one is being pummeled by the rapids. EMS says 2 people are trapped at the Brookside Inn and another person is trapped inside a home. Eversource is also here WTNH News 8

#BREAKING Two vehicles have been swept away by fast-moving floodwaters in Oxford. The rear tail lights of one is being pummeled by the rapids. EMS says 2 people are trapped at the Brookside Inn and another person is trapped inside a home. Eversource is also here WTNH News 8

Brittany Schaefer

162,424 Aufrufe • vor 2 Jahren

Three artificially intelligent (AI) generated videos showing highly objectionable visuals of Makkah and Madina, one of the holiest sites of Muslims, surfaced on social media platforms, mainly Instagram, on Friday. Posted by Rohit Kumar, a resident of Akhtiyarpur Manjhauli village in Patna, on his Instagram profile (click here), the video surfaced on Friday, July 17. In one video, Kumar appears in a saffron scarf and enters the Kaaba with a pig, which defecates on the floor. "Duniya mein pehla aadmi hoon, jo Makkah-Madinah mein suar (pig) laaya hoon. (I am the first person who has brought a pig inside Makkah-Madinah)." Another video depicts him entering Makkah-Madinah and showing a shivaling. And the third video shows ancient Hindu statues right inside the holy premises. Rohit Kumar has an Instagram following of 25.8K. He also has another ID (click here) in which he has just seven posts and followers.

The Siasat Daily

23,124 Aufrufe • vor 2 Monaten

When a drone applies a force at an angle to a cart resting on a level surface the force produces a horizontal pull that moves the cart forward and a vertical lift that lightens the load on the wheels, illustrating how vectors separate into independent effects along two perpendicular axes.

When a drone applies a force at an angle to a cart resting on a level surface the force produces a horizontal pull that moves the cart forward and a vertical lift that lightens the load on the wheels, illustrating how vectors separate into independent effects along two perpendicular axes.

Matheorems

12,817 Aufrufe • vor 4 Tagen

We live in an illusion, a simulation created by nonphysical electromagnetic waves collapsing into material reality, where your soul is trapped inside an energetic container that we call matter. There, it learns the lessons of Good and Evil necessary for its evolution. That is why the body is made of earth/dirt/matter, while the soul is made of fire, which is plasma. In Hinduism and Buddhism, this is represented by the Bhavachakra, or Wheel of Life, which depicts samsara, the cycle of death and rebirth in which the soul is “trapped” until it escapes the wheel after acquiring the knowledge of Good and Evil and attaining wisdom. The three poisons at the center of samsara are actually the northern constellations Draco, Cygnus, and Ursa Major, constantly chasing one another in a circle, symbolizing both the passage of time and the endless, repeating cycles. The twelve outer sections represent the twelve zodiac constellations. So yes, we live in an illusion, a simulation, but not an illusion created by AI, as in The Matrix. It is an illusion created by God for the purpose of the soul’s evolution.

We live in an illusion, a simulation created by nonphysical electromagnetic waves collapsing into material reality, where your soul is trapped inside an energetic container that we call matter. There, it learns the lessons of Good and Evil necessary for its evolution. That is why the body is made of earth/dirt/matter, while the soul is made of fire, which is plasma. In Hinduism and Buddhism, this is represented by the Bhavachakra, or Wheel of Life, which depicts samsara, the cycle of death and rebirth in which the soul is “trapped” until it escapes the wheel after acquiring the knowledge of Good and Evil and attaining wisdom. The three poisons at the center of samsara are actually the northern constellations Draco, Cygnus, and Ursa Major, constantly chasing one another in a circle, symbolizing both the passage of time and the endless, repeating cycles. The twelve outer sections represent the twelve zodiac constellations. So yes, we live in an illusion, a simulation, but not an illusion created by AI, as in The Matrix. It is an illusion created by God for the purpose of the soul’s evolution.

Open Minded Approach

104,639 Aufrufe • vor 1 Monat

This is extra innings in an elimination game in the B1G Tournament. Iowa trails Illinois 4-2 with the bases loaded, no outs. This slide by Kyle Huckstorf is ruled “interference”. Results in a DP & negates a run. One of the worst calls you’ll ever see.

This is extra innings in an elimination game in the B1G Tournament. Iowa trails Illinois 4-2 with the bases loaded, no outs. This slide by Kyle Huckstorf is ruled “interference”. Results in a DP & negates a run. One of the worst calls you’ll ever see.

Ben Stevens

375,978 Aufrufe • vor 2 Jahren

One of the most haunting moments of my life was visiting Auschwitz and standing inside the remaining gas chambers, where hundreds of thousands of Jews and others were murdered in a systematic way over years. What stays with you is not noise. It’s the silence. The emptiness of a place built for industrial killing. You stand there knowing that families were forced inside together, knowing exactly what was about to happen, watching children, parents, siblings, and friends disappear one by one. The walls are quiet now, but your mind fills in what history erased. This is the largest crime scene in human history.

One of the most haunting moments of my life was visiting Auschwitz and standing inside the remaining gas chambers, where hundreds of thousands of Jews and others were murdered in a systematic way over years. What stays with you is not noise. It’s the silence. The emptiness of a place built for industrial killing. You stand there knowing that families were forced inside together, knowing exactly what was about to happen, watching children, parents, siblings, and friends disappear one by one. The walls are quiet now, but your mind fills in what history erased. This is the largest crime scene in human history.

AP

42,320 Aufrufe • vor 8 Monaten

🚨Islamization of every institution in America marches on… This is exactly how the Muslim Brotherhood’s 1991 Explanatory Memorandum said it would happen. “A kind of grand Jihad in eliminating and destroying the Western civilization from within… sabotaging its miserable house by their hands and the hands of the believers.” They told us the plan: infiltrate every institution - government, schools, media, and yes… law enforcement. One uniform at a time. One badge at a time. One “just another officer” at a time. Look at him, black vest, “POLICE” across the back. Ordinary. Trusted. Already inside. While we sleep, they settle. While we call it “diversity,” they execute the Civilization-Jihadist Process. This is the plan in motion.

🚨Islamization of every institution in America marches on… This is exactly how the Muslim Brotherhood’s 1991 Explanatory Memorandum said it would happen. “A kind of grand Jihad in eliminating and destroying the Western civilization from within… sabotaging its miserable house by their hands and the hands of the believers.” They told us the plan: infiltrate every institution - government, schools, media, and yes… law enforcement. One uniform at a time. One badge at a time. One “just another officer” at a time. Look at him, black vest, “POLICE” across the back. Ordinary. Trusted. Already inside. While we sleep, they settle. While we call it “diversity,” they execute the Civilization-Jihadist Process. This is the plan in motion.

Amy Mek

30,294 Aufrufe • vor 1 Monat

This week Lebanon installed one of the largest statues of Jesus Christ in the Middle East. The statue stands 26 meters tall, with a 16 meter figure of Christ mounted on a 10 meter base, on Jabal al-Salib, which translates to Mount of the Cross, in the village of Al Qaa in the Bekaa Valley overlooking the Syrian border. The project was funded and built by local resident Fadi Elias Awad in cooperation with the Al Qaa municipality. Al Qaa is one of the oldest Christian communities in the region, populated mainly by Maronite and Greek Catholic families. The village was previously on the direct frontline with *S*S and was targeted by a terrorist bombing at its church. The statue was described by residents as a symbol of Christian presence, faith, and resilience on their land. The wider religious site including a church is still under construction. Credit: sacredchad for editing this video

This week Lebanon installed one of the largest statues of Jesus Christ in the Middle East. The statue stands 26 meters tall, with a 16 meter figure of Christ mounted on a 10 meter base, on Jabal al-Salib, which translates to Mount of the Cross, in the village of Al Qaa in the Bekaa Valley overlooking the Syrian border. The project was funded and built by local resident Fadi Elias Awad in cooperation with the Al Qaa municipality. Al Qaa is one of the oldest Christian communities in the region, populated mainly by Maronite and Greek Catholic families. The village was previously on the direct frontline with SS and was targeted by a terrorist bombing at its church. The statue was described by residents as a symbol of Christian presence, faith, and resilience on their land. The wider religious site including a church is still under construction. Credit: sacredchad for editing this video

Trad West

19,692 Aufrufe • vor 6 Monaten

⚡️Iranian Fars Agency: Second Lieutenant Colonel Shahin Dehghan, one of the police officers of Malard County, west of Tehran Province, was stabbed to death with a knife by rioters (photo) In another development, An Iranian Baloch armed group called Jaish al-Adl claimed responsibility and released documentation of the assassination of the deputy police commander in the city of Iranshahr inside Iran (video)

⚡️Iranian Fars Agency: Second Lieutenant Colonel Shahin Dehghan, one of the police officers of Malard County, west of Tehran Province, was stabbed to death with a knife by rioters (photo) In another development, An Iranian Baloch armed group called Jaish al-Adl claimed responsibility and released documentation of the assassination of the deputy police commander in the city of Iranshahr inside Iran (video)

Warfare Analysis

40,540 Aufrufe • vor 8 Monaten

As a gynecologist, one of the most frequently asked questions is about the ''hymen''. The hymen is not a structure located deep inside the vagina. It is a thin, flexible fold of tissue situated very close to the vaginal opening, anatomically at the entrance of the vaginal canal. It is typically found about 1–2 cm inside the vaginal opening, but in many women, it is almost at the surface. Therefore, the common belief that it is located deep inside is incorrect. One of the most important points is this: The hymen is not a closed membrane. It naturally has openings that allow menstrual blood to pass. Additionally, the structure of the hymen varies from person to person. Its thickness, elasticity, and shape are not standard. In some women, it may be very thin and elastic, while in others, it may be minimal or barely noticeable. This is completely a normal anatomical variation. A common misconception is that changes in the hymen occur only due to sexual intercourse. In reality, factors such as certain physical activities or tampon use can also lead to stretching or changes in this tissue. Therefore, the hymen is not a reliable indicator of a person’s sexual history or “virginity.” In summary, the hymen is a small and variable anatomical structure. The meanings attributed to it are largely shaped by sociocultural beliefs rather than medical facts.

As a gynecologist, one of the most frequently asked questions is about the ''hymen''. The hymen is not a structure located deep inside the vagina. It is a thin, flexible fold of tissue situated very close to the vaginal opening, anatomically at the entrance of the vaginal canal. It is typically found about 1–2 cm inside the vaginal opening, but in many women, it is almost at the surface. Therefore, the common belief that it is located deep inside is incorrect. One of the most important points is this: The hymen is not a closed membrane. It naturally has openings that allow menstrual blood to pass. Additionally, the structure of the hymen varies from person to person. Its thickness, elasticity, and shape are not standard. In some women, it may be very thin and elastic, while in others, it may be minimal or barely noticeable. This is completely a normal anatomical variation. A common misconception is that changes in the hymen occur only due to sexual intercourse. In reality, factors such as certain physical activities or tampon use can also lead to stretching or changes in this tissue. Therefore, the hymen is not a reliable indicator of a person’s sexual history or “virginity.” In summary, the hymen is a small and variable anatomical structure. The meanings attributed to it are largely shaped by sociocultural beliefs rather than medical facts.

Op. Dr. Mehmet Bekir Şen

597,069 Aufrufe • vor 23 Tagen

Yellow jackets, which usually nest underground and are often disturbed by a lawn mower or chainsaw, are one of the most dangerous and aggressive insects around. (Haven’t done an Entomology post lately so figured I’d throw one on) Why are they so dangerous? Because they can rapidly and repeatedly sting. This is a video I took of one who had attacked a katydid. As you can see, even as the yellow jacket begins to feed on the katydid, he continues to rapidly “pop” the prey with his stinger, pumping the paralyzing venom into the katydid. I count around 10 full stings of the prey. When a person is stung by a yellow jacket the first time, it releases an “alert pheromone”, which signals to most of the other colony members that danger is present. A major swarm of yellow jackets will then proceed out of the nest and attack the person (or animal). It takes around 1500 stings to kill a grown adult and 300-400 to kill a child. These numbers are achieved quickly with 100-200 yellow jackets swarming. If a person is allergic, they can go into anaphylactic shock with just one sting. I’m all about “saving the bees” because of their pollination factor…but Yellowjackets are one species of insect that I would gladly eliminate because of their danger. If you see them flying around the ground, or a tree stump or some rail road ties in the landscape, avoid them at all costs.

Yellow jackets, which usually nest underground and are often disturbed by a lawn mower or chainsaw, are one of the most dangerous and aggressive insects around. (Haven’t done an Entomology post lately so figured I’d throw one on) Why are they so dangerous? Because they can rapidly and repeatedly sting. This is a video I took of one who had attacked a katydid. As you can see, even as the yellow jacket begins to feed on the katydid, he continues to rapidly “pop” the prey with his stinger, pumping the paralyzing venom into the katydid. I count around 10 full stings of the prey. When a person is stung by a yellow jacket the first time, it releases an “alert pheromone”, which signals to most of the other colony members that danger is present. A major swarm of yellow jackets will then proceed out of the nest and attack the person (or animal). It takes around 1500 stings to kill a grown adult and 300-400 to kill a child. These numbers are achieved quickly with 100-200 yellow jackets swarming. If a person is allergic, they can go into anaphylactic shock with just one sting. I’m all about “saving the bees” because of their pollination factor…but Yellowjackets are one species of insect that I would gladly eliminate because of their danger. If you see them flying around the ground, or a tree stump or some rail road ties in the landscape, avoid them at all costs.

BowTiedBroke

2,209,187 Aufrufe • vor 2 Jahren