To read this article, scroll down the page to reach the article
While a 3D complex number would ... more To read this article, scroll down the page to reach the article
While a 3D complex number would be useful, it does not exist. Recently, I have constructed the N-complex number, which has demonstrated high efficiency in computations involving high-dimensional geometry. The N-complex number provides arithmetic operations and polar coordinates for N-dimensional spaces, akin to the classic complex number. In this paper, we will explain how these systems work and present studies on 4D Klein bottles and hyperspheres to illustrate the advantages of these systems
The walls of Tokamaks are heavily eroded by plasma which suggests that a mysterious force pushes ... more The walls of Tokamaks are heavily eroded by plasma which suggests that a mysterious force pushes the plasma to the wall. We have theoretically discovered this force and named it extra-force. This force appears only on single charges but not on current carrying wire, which is why the Lorentz force law does not contain it. This discovery not only brings new knowledge to electromagnetism, but also gives a solution against the erosion, which could improve the technology for controlled nuclear fusion. We have proposed an experiment to test this new force.
To read this article, just scroll down in the page of the article.
Normal physicists believe tha... more To read this article, just scroll down in the page of the article.
Normal physicists believe that Maxwell's theory is flawless and think that any challenge to it is absurd. However, we have shown in « From Coulomb's force to magnetic force and experiments that show parallel-to-current magnetic force » 1 that the prediction of the Lorentz force law is wrong and that the new magnetic force law derived in this article gives the correct magnetic force. Since the Lorentz force law is wrong, the energy and mass of high energy particles which are derived with this law are unreliable. Also, the magnetic confinement of plasma in Tokamak does not work as the Lorentz force law predicts and fails.
To read this article, just scroll down in the page of the article.
It is known long ago that t... more To read this article, just scroll down in the page of the article.
It is known long ago that the Lorentz forces between two current elements do not respect the Newton's third law. In physical sciences a discrepancy often hides new understanding or unexpected breakthrough. For solving this problem, we give a pure theoretical derivation of magnetic force which respects the Newton's third law. This new law reveals how electric force is transformed into magnetic force by velocity which is supported by experimental evidence.
Hilbert's Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodat... more Hilbert's Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodate additional guests. But our analyze finds that this is not true.
The apparent non-gravitational acceleration the extra-solar-system 'Oumuamua exhibits is puzzling... more The apparent non-gravitational acceleration the extra-solar-system 'Oumuamua exhibits is puzzling. We find that when the position and velocity of the Sun is correctly set in computing the predicted orbit, 'Oumuamua's trajectory can be explained with gravity and we have reproduced the unexpected gap by computation. We also propose to search for new extrasolar-system high speed asteroids with SOHO to check our method with their trajectories.
The Induced conductor net problem could be solved if we can determine the induced voltage in part... more The Induced conductor net problem could be solved if we can determine the induced voltage in part of the circuit. But is it possible that a voltage exist in no-loop wire? Let us see what the induced voltage is in a circular loop formed with 4 segments separated by resistors
Etude de l'evolution thermomecanique du film de lubrifiant dans les paliers axiaux. Construct... more Etude de l'evolution thermomecanique du film de lubrifiant dans les paliers axiaux. Construction d'un modele numerique. Etude des deformations du patin et du collet
I have constructed a complex number system with 3 or more dimensions (for Download). Edgar Malino... more I have constructed a complex number system with 3 or more dimensions (for Download). Edgar Malinovsky used my 3D system to render 3D Mandelbrot set, Lambda set and corresponding Julia sets. I have assembled the most beautiful and representative images of these 3D objects in the present document.
The roll, pitch and yaw of an object relative to another is complex to compute. We use 3D complex... more The roll, pitch and yaw of an object relative to another is complex to compute. We use 3D complex number to compute them which makes the computation easier and more intuitive.
Cantor's diagonal argument shows that ℝ is uncountable. But our analysis shows that ℝ is in fact ... more Cantor's diagonal argument shows that ℝ is uncountable. But our analysis shows that ℝ is in fact the set of points on the number line which can be put into a list. We will explain what the property that supports uncountability really is and propose a new scheme to count points.
An analysis of Cantor’s theory of uncountable sets: The logic of his proofs has some weaknesses. ... more An analysis of Cantor’s theory of uncountable sets: The logic of his proofs has some weaknesses. Cantor assumes for both his proofs that all real numbers (set R) are in a list (list L). Considering L as a set this assumption gives R belongs to L. This makes the claim “a real number is constructed but is not in the list L” dubious. We propose a solution to this problem, an axiom for counting infinite sets and a solution to continuum hypothesis.
The Schwarzschild radius is the radius of the event horizon of a black hole. Amazingly, we can co... more The Schwarzschild radius is the radius of the event horizon of a black hole. Amazingly, we can compute it with Newtonian mechanics. The gravitational force on m approaches infinity near M. But the speed of m never reaches the speed of light c, which is true for any force however strong it is and for time of acceleration however long it is. How the Schwarzschild radius obey relativistic principle is explained.
Today's methods for computing orientation are quaternion and rotation matrix. However, their effi... more Today's methods for computing orientation are quaternion and rotation matrix. However, their efficiencies are tarnished by the complexity of the rotation matrix and the counterintuitivity of quaternion. A better method is presented here. It uses complex multiplication for rotating vectors in 3D space and can compute orientation without angle and trigonometric functions, which is simple, intuitive and fast.
Multidimensional complex systems with 3, 4 or more dimensions are constructed. They possess algeb... more Multidimensional complex systems with 3, 4 or more dimensions are constructed. They possess algebraic operations which have geometrical meanings. Multidimensional complex numbers can be written in Cartesian, trigonometric and exponential form and can be converted from one form to another. Each complex numbers has a conjugate. Multidimensional complex systems are extensions of the classical complex number system.
The orientation of body in space is defined 3 by angles. The step by step rotation process and ch... more The orientation of body in space is defined 3 by angles. The step by step rotation process and chain of three-dots multiplication give an easy way to compute pile of rotations in 3D and high dimensional space and give a general orientation system. A visualization of quaternion is proposed.
Orbital precession of the planet Mercury was computed using Space-Time curvature which is extreme... more Orbital precession of the planet Mercury was computed using Space-Time curvature which is extremely difficult to understand. This article exposes an analytical orbit equation for relativistic gravity and explains how it is derived without Space-Time geodesics. The value of orbital precession that this orbit equation gives is identical to that computed using General Relativity. This orbit equation is an analytical form of Space-Time geodesics for space objects and makes everyone able to compute the orbit of any object in gravitational field which obeys General Relativity using personal computer and its direct derivation from gravitational acceleration gives a new insight to General Relativity without the need of knowing Einstein tensor.
Special relativity does not deal with acceleration, general relativity does not deal with non gra... more Special relativity does not deal with acceleration, general relativity does not deal with non gravitational acceleration, which leave the theory of relativity imperfect. We will demonstrate some relativistic dynamical laws that specify relativistic acceleration, force and kinetic energy. Also, based on equivalence principle does gravitational mass vary with inertial mass?
To read this article, scroll down the page to reach the article
While a 3D complex number would ... more To read this article, scroll down the page to reach the article
While a 3D complex number would be useful, it does not exist. Recently, I have constructed the N-complex number, which has demonstrated high efficiency in computations involving high-dimensional geometry. The N-complex number provides arithmetic operations and polar coordinates for N-dimensional spaces, akin to the classic complex number. In this paper, we will explain how these systems work and present studies on 4D Klein bottles and hyperspheres to illustrate the advantages of these systems
The walls of Tokamaks are heavily eroded by plasma which suggests that a mysterious force pushes ... more The walls of Tokamaks are heavily eroded by plasma which suggests that a mysterious force pushes the plasma to the wall. We have theoretically discovered this force and named it extra-force. This force appears only on single charges but not on current carrying wire, which is why the Lorentz force law does not contain it. This discovery not only brings new knowledge to electromagnetism, but also gives a solution against the erosion, which could improve the technology for controlled nuclear fusion. We have proposed an experiment to test this new force.
To read this article, just scroll down in the page of the article.
Normal physicists believe tha... more To read this article, just scroll down in the page of the article.
Normal physicists believe that Maxwell's theory is flawless and think that any challenge to it is absurd. However, we have shown in « From Coulomb's force to magnetic force and experiments that show parallel-to-current magnetic force » 1 that the prediction of the Lorentz force law is wrong and that the new magnetic force law derived in this article gives the correct magnetic force. Since the Lorentz force law is wrong, the energy and mass of high energy particles which are derived with this law are unreliable. Also, the magnetic confinement of plasma in Tokamak does not work as the Lorentz force law predicts and fails.
To read this article, just scroll down in the page of the article.
It is known long ago that t... more To read this article, just scroll down in the page of the article.
It is known long ago that the Lorentz forces between two current elements do not respect the Newton's third law. In physical sciences a discrepancy often hides new understanding or unexpected breakthrough. For solving this problem, we give a pure theoretical derivation of magnetic force which respects the Newton's third law. This new law reveals how electric force is transformed into magnetic force by velocity which is supported by experimental evidence.
Hilbert's Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodat... more Hilbert's Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodate additional guests. But our analyze finds that this is not true.
The apparent non-gravitational acceleration the extra-solar-system 'Oumuamua exhibits is puzzling... more The apparent non-gravitational acceleration the extra-solar-system 'Oumuamua exhibits is puzzling. We find that when the position and velocity of the Sun is correctly set in computing the predicted orbit, 'Oumuamua's trajectory can be explained with gravity and we have reproduced the unexpected gap by computation. We also propose to search for new extrasolar-system high speed asteroids with SOHO to check our method with their trajectories.
The Induced conductor net problem could be solved if we can determine the induced voltage in part... more The Induced conductor net problem could be solved if we can determine the induced voltage in part of the circuit. But is it possible that a voltage exist in no-loop wire? Let us see what the induced voltage is in a circular loop formed with 4 segments separated by resistors
Etude de l'evolution thermomecanique du film de lubrifiant dans les paliers axiaux. Construct... more Etude de l'evolution thermomecanique du film de lubrifiant dans les paliers axiaux. Construction d'un modele numerique. Etude des deformations du patin et du collet
I have constructed a complex number system with 3 or more dimensions (for Download). Edgar Malino... more I have constructed a complex number system with 3 or more dimensions (for Download). Edgar Malinovsky used my 3D system to render 3D Mandelbrot set, Lambda set and corresponding Julia sets. I have assembled the most beautiful and representative images of these 3D objects in the present document.
The roll, pitch and yaw of an object relative to another is complex to compute. We use 3D complex... more The roll, pitch and yaw of an object relative to another is complex to compute. We use 3D complex number to compute them which makes the computation easier and more intuitive.
Cantor's diagonal argument shows that ℝ is uncountable. But our analysis shows that ℝ is in fact ... more Cantor's diagonal argument shows that ℝ is uncountable. But our analysis shows that ℝ is in fact the set of points on the number line which can be put into a list. We will explain what the property that supports uncountability really is and propose a new scheme to count points.
An analysis of Cantor’s theory of uncountable sets: The logic of his proofs has some weaknesses. ... more An analysis of Cantor’s theory of uncountable sets: The logic of his proofs has some weaknesses. Cantor assumes for both his proofs that all real numbers (set R) are in a list (list L). Considering L as a set this assumption gives R belongs to L. This makes the claim “a real number is constructed but is not in the list L” dubious. We propose a solution to this problem, an axiom for counting infinite sets and a solution to continuum hypothesis.
The Schwarzschild radius is the radius of the event horizon of a black hole. Amazingly, we can co... more The Schwarzschild radius is the radius of the event horizon of a black hole. Amazingly, we can compute it with Newtonian mechanics. The gravitational force on m approaches infinity near M. But the speed of m never reaches the speed of light c, which is true for any force however strong it is and for time of acceleration however long it is. How the Schwarzschild radius obey relativistic principle is explained.
Today's methods for computing orientation are quaternion and rotation matrix. However, their effi... more Today's methods for computing orientation are quaternion and rotation matrix. However, their efficiencies are tarnished by the complexity of the rotation matrix and the counterintuitivity of quaternion. A better method is presented here. It uses complex multiplication for rotating vectors in 3D space and can compute orientation without angle and trigonometric functions, which is simple, intuitive and fast.
Multidimensional complex systems with 3, 4 or more dimensions are constructed. They possess algeb... more Multidimensional complex systems with 3, 4 or more dimensions are constructed. They possess algebraic operations which have geometrical meanings. Multidimensional complex numbers can be written in Cartesian, trigonometric and exponential form and can be converted from one form to another. Each complex numbers has a conjugate. Multidimensional complex systems are extensions of the classical complex number system.
The orientation of body in space is defined 3 by angles. The step by step rotation process and ch... more The orientation of body in space is defined 3 by angles. The step by step rotation process and chain of three-dots multiplication give an easy way to compute pile of rotations in 3D and high dimensional space and give a general orientation system. A visualization of quaternion is proposed.
Orbital precession of the planet Mercury was computed using Space-Time curvature which is extreme... more Orbital precession of the planet Mercury was computed using Space-Time curvature which is extremely difficult to understand. This article exposes an analytical orbit equation for relativistic gravity and explains how it is derived without Space-Time geodesics. The value of orbital precession that this orbit equation gives is identical to that computed using General Relativity. This orbit equation is an analytical form of Space-Time geodesics for space objects and makes everyone able to compute the orbit of any object in gravitational field which obeys General Relativity using personal computer and its direct derivation from gravitational acceleration gives a new insight to General Relativity without the need of knowing Einstein tensor.
Special relativity does not deal with acceleration, general relativity does not deal with non gra... more Special relativity does not deal with acceleration, general relativity does not deal with non gravitational acceleration, which leave the theory of relativity imperfect. We will demonstrate some relativistic dynamical laws that specify relativistic acceleration, force and kinetic energy. Also, based on equivalence principle does gravitational mass vary with inertial mass?
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Papers by Kuan Peng
While a 3D complex number would be useful, it does not exist. Recently, I have constructed the N-complex number, which has demonstrated high efficiency in computations involving high-dimensional geometry. The N-complex number provides arithmetic operations and polar coordinates for N-dimensional spaces, akin to the classic complex number. In this paper, we will explain how these systems work and present studies on 4D Klein bottles and hyperspheres to illustrate the advantages of these systems
Normal physicists believe that Maxwell's theory is flawless and think that any challenge to it is absurd. However, we have shown in « From Coulomb's force to magnetic force and experiments that show parallel-to-current magnetic force » 1 that the prediction of the Lorentz force law is wrong and that the new magnetic force law derived in this article gives the correct magnetic force. Since the Lorentz force law is wrong, the energy and mass of high energy particles which are derived with this law are unreliable. Also, the magnetic confinement of plasma in Tokamak does not work as the Lorentz force law predicts and fails.
It is known long ago that the Lorentz forces between two current elements do not respect the Newton's third law. In physical sciences a discrepancy often hides new understanding or unexpected breakthrough. For solving this problem, we give a pure theoretical derivation of magnetic force which respects the Newton's third law. This new law reveals how electric force is transformed into magnetic force by velocity which is supported by experimental evidence.
While a 3D complex number would be useful, it does not exist. Recently, I have constructed the N-complex number, which has demonstrated high efficiency in computations involving high-dimensional geometry. The N-complex number provides arithmetic operations and polar coordinates for N-dimensional spaces, akin to the classic complex number. In this paper, we will explain how these systems work and present studies on 4D Klein bottles and hyperspheres to illustrate the advantages of these systems
Normal physicists believe that Maxwell's theory is flawless and think that any challenge to it is absurd. However, we have shown in « From Coulomb's force to magnetic force and experiments that show parallel-to-current magnetic force » 1 that the prediction of the Lorentz force law is wrong and that the new magnetic force law derived in this article gives the correct magnetic force. Since the Lorentz force law is wrong, the energy and mass of high energy particles which are derived with this law are unreliable. Also, the magnetic confinement of plasma in Tokamak does not work as the Lorentz force law predicts and fails.
It is known long ago that the Lorentz forces between two current elements do not respect the Newton's third law. In physical sciences a discrepancy often hides new understanding or unexpected breakthrough. For solving this problem, we give a pure theoretical derivation of magnetic force which respects the Newton's third law. This new law reveals how electric force is transformed into magnetic force by velocity which is supported by experimental evidence.