Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more ...Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy’s maximum quantum entanglement probability as the fifth power of φand its connection to the dark matter. Remembering, the eleven dimensions in Witten’s M-theory may be decomposed into the Lucas number L5 = 11 = φ−5 – φ5. Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld’s fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.展开更多
This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”....This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.展开更多
The nature of gravitation and <em>G</em> is not well understood. A new gravitation mechanism is proposed that explains the origin and essence of the gravitational constant, <em>G</em>. Based on...The nature of gravitation and <em>G</em> is not well understood. A new gravitation mechanism is proposed that explains the origin and essence of the gravitational constant, <em>G</em>. Based on general relativity, the vacuum is considered to be a superfluid with measurable density. Rotating bodies drag vacuum and create a vortex with gradient pressure. The drag force of vacuum fluid flow in the arm of the vortex is calculated relative to the static vacuum and a value that is numerically equal to that of <em>G</em> is obtained. Using Archimedes’ principle, it is determined that <em>G</em> is the volume of vacuum displaced by a force equivalent to its weight which is equal to the drag force of the vacuum. It is concluded that the gravitational constant <em>G</em> expresses the force needed to displace a cubic metre of vacuum that weighs one kg in one second. Therefore, <em>G</em> is not a fundamental physical constant but rather is an expression of the resistance encountered by the gravitational force in the vacuum.展开更多
The drag on non-spherical particles is an important basic parameter for multi-phase flows such as in biomass combustion, chemical blending, and mineral processing. Though there is much experimental research on such pa...The drag on non-spherical particles is an important basic parameter for multi-phase flows such as in biomass combustion, chemical blending, and mineral processing. Though there is much experimental research on such particles, there are few results for cuboids. This paper presents data for cuboids with a square base in static glycerin-water solutions of various volume concentrations. Complex motions were observed and characterized. A dimensionless expression is given for terminal velocity ut as a function of Archimedes number Ar which is used to develop an accurate correlation for friction factor CD. The accuracy of the correlation is 7.9% compared to experimental data in the literature. For both square plates and square rods, the terminal velocity per unit mass, ut/mp, was used to characterize the influence of narticle geometry on velocity, which was shown to be linear.展开更多
In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-t...In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.展开更多
Different from sculling forward of water striders with their hairy water-repellent legs, water spiders walked very quickly on water surfaces. By using a shadow method, the walking of water spiders had been studied. Th...Different from sculling forward of water striders with their hairy water-repellent legs, water spiders walked very quickly on water surfaces. By using a shadow method, the walking of water spiders had been studied. The three-dimensional trajectories and the supporting forces of water spider legs during walking forward were achieved. Results showed that the leg movement could be divided into three phases： slap, stroke, and retrieve. Employing an effective strategy to improving walking efficiency, the sculling legs supported most of its body weight while other legs were lifted to reduce the lateral water resistance, which was similar to the strategy of water striders. These findings could help guiding the design of water walking robots with high efficiency.展开更多
In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matte...In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.展开更多
A combined experimental and numerical research study is conducted to investigate the complex relationship between the structure and the aerodynamic performances of an Archimedes spiral wind turbine(ASWT).Two ASWTs are...A combined experimental and numerical research study is conducted to investigate the complex relationship between the structure and the aerodynamic performances of an Archimedes spiral wind turbine(ASWT).Two ASWTs are considered,a prototypical version and an improved version.It is shown that the latter achieves the best aerodynamic performance when the spread angles at the three sets of blades areα_(1)=30°,α_(2)=55°,α3=60°,respectively and the blade thickness is 4 mm.For a velocity V=10 m/s,a tip speed ratio(TSR)=1.58 and 2,the maximum CP values are 0.223 and 0.263 for the prototypical ASWT and improved ASWT,respectively,and the maximum C_(P) enhancement is 17.93%.For V=10 m/s and TSR=2,the CP values of the prototypical ASWT and improved ASWT are 0.225 and 0.263,respectively,with an aerodynamic performance enhancement of 16.88%.Through mutual verification of the test outcomes and numerical results,it is concluded that the proposed approach can effectively lead to aerodynamic performance improvement.展开更多
This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using ...This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm<sup>2</sup>. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.展开更多
This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach ...This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.展开更多
This work is devoted to the study of the relationship between strong earthquakes and planetary configurations using the example of two consecutive strong earthquakes that occurred in Türkiye (Turkey), on February...This work is devoted to the study of the relationship between strong earthquakes and planetary configurations using the example of two consecutive strong earthquakes that occurred in Türkiye (Turkey), on February 6, 2023. It is shown that at the time of the earthquakes, linear alignment of the planets along the Jupiter-Venus-Sun line was observed, that is, the astronomical trigger belonged to the generalized Kepler conjunction scheme (gKc), when the Earth does not participate in the linearization scheme. It is shown that for the first earthquake that occurred at 01:17 UTC, the ratio of the distances between Jupiter-Earth and Jupiter-Mars was close to an integer value equal to 5.993. For the second earthquake that occurred on the same day at 10:25 UTC, no integer resonance ratios were detected, however, it was found that the terrestrial e UTC line at the time of the earthquake passed through the position of Mercury. Recall that the 12-hour line of the eUTC chart is always oriented towards the Sun. The conclusions of the work once again confirm the correctness of the theories of Archimedes and Kepler and convince us of the existence of a gravitational phenomenon that does not depend on the distances and masses of planets, has a pronounced inertial and wave character and does not fit into the general theory of relativity, developed in the last century by Albert Einstein.展开更多
It has been shown that it is possible to produce thin wall ductile iron (TWDI) castings of considerable length using an Archimedes spirals with a wall of 1, 2 or 3 mm in thickness. The fluidities for different mouldin...It has been shown that it is possible to produce thin wall ductile iron (TWDI) castings of considerable length using an Archimedes spirals with a wall of 1, 2 or 3 mm in thickness. The fluidities for different moulding materials [(classical mould, chemically bonded silica sand and chemically bonded low-density alumina-silicate ceramic sand (LDASC)], chemical composition, and pouring temperature were estimated. There is a significant temperature drop in thin sections (contrary to typical sections) during the mould filling. A profile of real temperature drop is presented along with theoretical predictions. The high temperature drop of liquid iron results in an increased cooling rate (before the eutectic equilibrium solidification temperature), which in turn affects the solidification and microstructure of TWDI castings. Microstructures were characterized quantitatively using an image analyser. Structure parameters for different wall thicknesses and moulding materials (graphite nodule count, ferrite and cementite fraction) are plotted, which is versus distance from the entrance to the mould cavity. It has been shown that the thin wall castings have a gradient structure. Moreover, a strong influence of LDASC sand (material with low ability to absorb the heat) on the structure parameters of TWDI castings is presented.展开更多
This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when...This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angles were found to be 10.00000˚ and 20.00000˚ respectively (i.e. exactly one-third of the given angle or ∠E’MA = 1/3∠E’CG). Based on this identical angular relationship as well as the numerical results obtained, one can only conclude that the geometric requirements for arriving at an exact trisection of the 30˚ or 60˚ angle, and therefore the construction of a 10˚ or 20˚ angle, have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others. Thus, the solution to the age-old trisection problem, with respect to these two angles, has been accomplished.展开更多
A new dynamic equation of aerosol in air is derived, using a model-in-model, by equilibrium of buoyancy, gravity and pressure, together with conservation laws of mass, momentum and energy via Reynolds transport theore...A new dynamic equation of aerosol in air is derived, using a model-in-model, by equilibrium of buoyancy, gravity and pressure, together with conservation laws of mass, momentum and energy via Reynolds transport theorem and supplemented by corresponding scientific laws for related properties of air and aerosols. This new dynamic equation of aerosol in air is a set of non-linear partial differential equations involved six unknown functions of mass densities, pressure, air and aerosol speeds and temperature. It has features: 1, it belongs to certain type;2, it emphases the effect of buoyancy in equilibrium and potential energy, and the Archimedes principle of buoyancy is firstly extended to lateral directions based on logical deduction, the phenomenon of stirring a glass of oil-water mixture and the recorded of Hurricane Isabel (2003) from space station. The later shows the evidence of existence of lateral buoyancy;3, the mass densities of air and aerosol of a point in our model are varied in different directions due to traction and are treated as vectors, and they have been used in the calculation of lateral buoyancy.展开更多
Based on Newton’s third law of motion, we present a different but quite general analysis of Archimedes’ principle. This analysis explains the reduction in apparent weight of a submerged object in all cases, regardle...Based on Newton’s third law of motion, we present a different but quite general analysis of Archimedes’ principle. This analysis explains the reduction in apparent weight of a submerged object in all cases, regardless of its position in the fluid. We also study the case in which the object rests on the bottom of the container where the net hydrostatic force on it is downward, and explain where in this case the reduction in the apparent weight comes from.展开更多
Following a brief review of the “black hole dark energy radiation” and “gravitized vacuum” references, a novel theory of how gravity might affect the quantum vacuum is proposed. This overarching theory proposes th...Following a brief review of the “black hole dark energy radiation” and “gravitized vacuum” references, a novel theory of how gravity might affect the quantum vacuum is proposed. This overarching theory proposes that the gravitational field of a sufficiently concentrated collection of matter and/or energy upregulates the virtual particle activity of the adjacent quantum vacuum, thus its energy density and lensing capacity. In contrast to general relativity, the particle and wave duality of quantum physics is necessary for understanding quantum vacuum gravitational effects. Very recent supporting and pending observational studies are discussed, including the ingenious and extremely sensitive vacuum scale to be deployed for the Archimedes Experiment. Support or falsification of this proposal may be imminent.展开更多
This paper presents a graphical procedure, using an unmarked straightedge and compass only, for trisecting an arbitrary acute angle. The procedure, when applied to the 30˚angle that has been “proven” to be ...This paper presents a graphical procedure, using an unmarked straightedge and compass only, for trisecting an arbitrary acute angle. The procedure, when applied to the 30˚angle that has been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angle was found to be exactly one-third of the given angle (or ∠E'MA = 1/3∠E'CG = 10˚), as shown in Figure 1(D) and Figure 1(E) and Section 4 PROOF in this paper. Hence, based on this identical angular relationship between the construction presented and Archimedes’ Construction, one can only conclude that geometric requirements for arriving at an exact trisection have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others.展开更多
文摘Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy’s maximum quantum entanglement probability as the fifth power of φand its connection to the dark matter. Remembering, the eleven dimensions in Witten’s M-theory may be decomposed into the Lucas number L5 = 11 = φ−5 – φ5. Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld’s fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.
文摘This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.
文摘The nature of gravitation and <em>G</em> is not well understood. A new gravitation mechanism is proposed that explains the origin and essence of the gravitational constant, <em>G</em>. Based on general relativity, the vacuum is considered to be a superfluid with measurable density. Rotating bodies drag vacuum and create a vortex with gradient pressure. The drag force of vacuum fluid flow in the arm of the vortex is calculated relative to the static vacuum and a value that is numerically equal to that of <em>G</em> is obtained. Using Archimedes’ principle, it is determined that <em>G</em> is the volume of vacuum displaced by a force equivalent to its weight which is equal to the drag force of the vacuum. It is concluded that the gravitational constant <em>G</em> expresses the force needed to displace a cubic metre of vacuum that weighs one kg in one second. Therefore, <em>G</em> is not a fundamental physical constant but rather is an expression of the resistance encountered by the gravitational force in the vacuum.
基金supported by the Major Program of the National Natural Science Foundation of China with Grant No. 10632070
文摘The drag on non-spherical particles is an important basic parameter for multi-phase flows such as in biomass combustion, chemical blending, and mineral processing. Though there is much experimental research on such particles, there are few results for cuboids. This paper presents data for cuboids with a square base in static glycerin-water solutions of various volume concentrations. Complex motions were observed and characterized. A dimensionless expression is given for terminal velocity ut as a function of Archimedes number Ar which is used to develop an accurate correlation for friction factor CD. The accuracy of the correlation is 7.9% compared to experimental data in the literature. For both square plates and square rods, the terminal velocity per unit mass, ut/mp, was used to characterize the influence of narticle geometry on velocity, which was shown to be linear.
文摘In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51323006 and 51425502)the Tribology Science Fund of State Key Laboratory of Tribology(Grant No.SKLTKF17B18)
文摘Different from sculling forward of water striders with their hairy water-repellent legs, water spiders walked very quickly on water surfaces. By using a shadow method, the walking of water spiders had been studied. The three-dimensional trajectories and the supporting forces of water spider legs during walking forward were achieved. Results showed that the leg movement could be divided into three phases： slap, stroke, and retrieve. Employing an effective strategy to improving walking efficiency, the sculling legs supported most of its body weight while other legs were lifted to reduce the lateral water resistance, which was similar to the strategy of water striders. These findings could help guiding the design of water walking robots with high efficiency.
文摘In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.
基金supported by the National Natural Science Foundation of China.Project under Grant(Nos.51966018 and 51466015).
文摘A combined experimental and numerical research study is conducted to investigate the complex relationship between the structure and the aerodynamic performances of an Archimedes spiral wind turbine(ASWT).Two ASWTs are considered,a prototypical version and an improved version.It is shown that the latter achieves the best aerodynamic performance when the spread angles at the three sets of blades areα_(1)=30°,α_(2)=55°,α3=60°,respectively and the blade thickness is 4 mm.For a velocity V=10 m/s,a tip speed ratio(TSR)=1.58 and 2,the maximum CP values are 0.223 and 0.263 for the prototypical ASWT and improved ASWT,respectively,and the maximum C_(P) enhancement is 17.93%.For V=10 m/s and TSR=2,the CP values of the prototypical ASWT and improved ASWT are 0.225 and 0.263,respectively,with an aerodynamic performance enhancement of 16.88%.Through mutual verification of the test outcomes and numerical results,it is concluded that the proposed approach can effectively lead to aerodynamic performance improvement.
文摘This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm<sup>2</sup>. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.
文摘This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.
文摘This work is devoted to the study of the relationship between strong earthquakes and planetary configurations using the example of two consecutive strong earthquakes that occurred in Türkiye (Turkey), on February 6, 2023. It is shown that at the time of the earthquakes, linear alignment of the planets along the Jupiter-Venus-Sun line was observed, that is, the astronomical trigger belonged to the generalized Kepler conjunction scheme (gKc), when the Earth does not participate in the linearization scheme. It is shown that for the first earthquake that occurred at 01:17 UTC, the ratio of the distances between Jupiter-Earth and Jupiter-Mars was close to an integer value equal to 5.993. For the second earthquake that occurred on the same day at 10:25 UTC, no integer resonance ratios were detected, however, it was found that the terrestrial e UTC line at the time of the earthquake passed through the position of Mercury. Recall that the 12-hour line of the eUTC chart is always oriented towards the Sun. The conclusions of the work once again confirm the correctness of the theories of Archimedes and Kepler and convince us of the existence of a gravitational phenomenon that does not depend on the distances and masses of planets, has a pronounced inertial and wave character and does not fit into the general theory of relativity, developed in the last century by Albert Einstein.
文摘It has been shown that it is possible to produce thin wall ductile iron (TWDI) castings of considerable length using an Archimedes spirals with a wall of 1, 2 or 3 mm in thickness. The fluidities for different moulding materials [(classical mould, chemically bonded silica sand and chemically bonded low-density alumina-silicate ceramic sand (LDASC)], chemical composition, and pouring temperature were estimated. There is a significant temperature drop in thin sections (contrary to typical sections) during the mould filling. A profile of real temperature drop is presented along with theoretical predictions. The high temperature drop of liquid iron results in an increased cooling rate (before the eutectic equilibrium solidification temperature), which in turn affects the solidification and microstructure of TWDI castings. Microstructures were characterized quantitatively using an image analyser. Structure parameters for different wall thicknesses and moulding materials (graphite nodule count, ferrite and cementite fraction) are plotted, which is versus distance from the entrance to the mould cavity. It has been shown that the thin wall castings have a gradient structure. Moreover, a strong influence of LDASC sand (material with low ability to absorb the heat) on the structure parameters of TWDI castings is presented.
文摘This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angles were found to be 10.00000˚ and 20.00000˚ respectively (i.e. exactly one-third of the given angle or ∠E’MA = 1/3∠E’CG). Based on this identical angular relationship as well as the numerical results obtained, one can only conclude that the geometric requirements for arriving at an exact trisection of the 30˚ or 60˚ angle, and therefore the construction of a 10˚ or 20˚ angle, have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others. Thus, the solution to the age-old trisection problem, with respect to these two angles, has been accomplished.
文摘A new dynamic equation of aerosol in air is derived, using a model-in-model, by equilibrium of buoyancy, gravity and pressure, together with conservation laws of mass, momentum and energy via Reynolds transport theorem and supplemented by corresponding scientific laws for related properties of air and aerosols. This new dynamic equation of aerosol in air is a set of non-linear partial differential equations involved six unknown functions of mass densities, pressure, air and aerosol speeds and temperature. It has features: 1, it belongs to certain type;2, it emphases the effect of buoyancy in equilibrium and potential energy, and the Archimedes principle of buoyancy is firstly extended to lateral directions based on logical deduction, the phenomenon of stirring a glass of oil-water mixture and the recorded of Hurricane Isabel (2003) from space station. The later shows the evidence of existence of lateral buoyancy;3, the mass densities of air and aerosol of a point in our model are varied in different directions due to traction and are treated as vectors, and they have been used in the calculation of lateral buoyancy.
文摘Based on Newton’s third law of motion, we present a different but quite general analysis of Archimedes’ principle. This analysis explains the reduction in apparent weight of a submerged object in all cases, regardless of its position in the fluid. We also study the case in which the object rests on the bottom of the container where the net hydrostatic force on it is downward, and explain where in this case the reduction in the apparent weight comes from.
文摘Following a brief review of the “black hole dark energy radiation” and “gravitized vacuum” references, a novel theory of how gravity might affect the quantum vacuum is proposed. This overarching theory proposes that the gravitational field of a sufficiently concentrated collection of matter and/or energy upregulates the virtual particle activity of the adjacent quantum vacuum, thus its energy density and lensing capacity. In contrast to general relativity, the particle and wave duality of quantum physics is necessary for understanding quantum vacuum gravitational effects. Very recent supporting and pending observational studies are discussed, including the ingenious and extremely sensitive vacuum scale to be deployed for the Archimedes Experiment. Support or falsification of this proposal may be imminent.
文摘This paper presents a graphical procedure, using an unmarked straightedge and compass only, for trisecting an arbitrary acute angle. The procedure, when applied to the 30˚angle that has been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angle was found to be exactly one-third of the given angle (or ∠E'MA = 1/3∠E'CG = 10˚), as shown in Figure 1(D) and Figure 1(E) and Section 4 PROOF in this paper. Hence, based on this identical angular relationship between the construction presented and Archimedes’ Construction, one can only conclude that geometric requirements for arriving at an exact trisection have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others.
