Happytummy. Toogoodtobetrue. Reinhabit sandiego. Current/Upcoming Call Menu. Harrison Hawkins and Florence Huntley. The life of Harrison Hawkins, father of the Rev. M.E. Hawkins, has not been nearly as well-known in the family as the ancestors of the daughter-in-law he never knew, Fern Porter Hawkins. In fact, until 1992, even the fact that his name was Harrison was not known to the family. An inquiry a few years earlier at the Greenwood Cemetery in Grand Rapids where he is buried offered the name “Hanson” (which was eventually proven to be erroneous).
We knew that Grandpa Hawkins’s father had fought for the Union in the Civil War. An intriguing piece of information about what took Harrison into the Union Army in the early days of the Civil War did not come from the Archives. If this is true, then Grandpa Hawkins apparently kept that information pretty close to his heart.
Among the papers from the Archives are Harrison’s death certificate (needed for his widow to lay claim to his pension) and the record of a second marriage ten years before his death. At enlistment: (July 4, 1861) 17 . . . No Obstacles. ONE OF THE interesting discoveries that is made by the average Student, early in his progress, is the fact that during his lifetime he has been accumulating a considerable fund of supposed knowledge, which in the light of a deeper insight into the Laws of Nature, is found to be based upon surmise, conjecture or misunderstanding.
Oftentimes these mistaken points of view have proven real obstacles in his efforts to develop his capabilities. Unconsciously, perhaps, he has been laboring against the Constructive Laws of Nature, instead of acting in conformity with them. It is an easy matter to take the wrong way at a crossroad, particularly if there is no guidepost. Then every step forward takes one that much further from his destination.
Thus, the Student finds that he has much to unlearn, as well as a great deal to learn. Acquisition of knowledge is a splendid thing, but knowledge is a burden unless it is rightly used. It is the unusual man or woman who really knows himself or herself. Course.cgi (application/pdf Object) Mathematics of Standing Waves. As discussed in Lesson 4, standing wave patterns are wave patterns produced in a medium when two waves of identical frequencies interfere in such a manner to produce points along the medium that always appear to be standing still.
Such standing wave patterns are produced within the medium when it is vibrated at certain frequencies. Each frequency is associated with a different standing wave pattern. These frequencies and their associated wave patterns are referred to as harmonics. A careful study of the standing wave patterns reveal a clear mathematical relationship between the wavelength of the wave that produces the pattern and the length of the medium in which the pattern is displayed. Furthermore, there is a predictability about this mathematical relationship that allows one to generalize and deduce a statement concerning this relationship. Analyzing the First Harmonic Pattern The pattern for the first harmonic reveals a single antinode in the middle of the rope. 1. 2. 3. 4. 5. The Mathematics of Music. The Pythagorean Scale is mathematically perfect in the relationship of the notes of the scale to the starting pitch, but it was soon discovered that this perfection created serious problems.
In the Pythagorean Scale we just created based on C, melodies and harmonies would sound beautiful if only those 7 notes, in different octaves, were used, i.e. the white keys, and C was always the tonal center. But suppose that we continued with the circle of p5th method and obtained the other notes, the black keys, and tried to use some other note than C as the tonal center. We would find that when we attempted to use another note as a tonal center, such as A-flat, it would sound badly out of tune. All the intervals would be perfect in relation to C, but quite imperfect in relation to A-flat. Every time you wanted to play in a different key, which had a different tonal center, you would have to re-tune the instruments, which is exactly what they had to do back in the 17th century. XII. XIII. XIV. Harmonics Theory Physics and Maths. Maxwell developed his famous equations for electromagnetism around 1870 and showed that not only electricty and magnetism behaved according to wave equations, but that interactions of the two also behaved as waves that travelled at the speed of light and produced the phenomena known as light, later found to include waves from long radio waves down to very short gamma ray waves.
Since then, major discoveries in fundamental physics have been dominated by the wave nature of all things, as shown by Einstein, Schroedinger, de Broglie and many others. Although the diverse phenomena modelled by the various physics equations have not yet been brought into the sphere of a single model, there are enough clues to say that such a model ought to be possible. It is natural that such a model would include a wave equation, and the universe is essentially a wave phenomenon. The question of whether the universe is finite or not is generally considered to still be open.
Math and Music. If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics. - George Santanaya Music is the pleasure of the human soul experiences from counting without being aware that it is counting. - Gottfried Leibniz Mathematics and music have a strange connection. Music is the only art form, where the form and the medium are the same. Mathematics is the only science where the methods and the subject are the same.
Mathematics is the study of mathematics using mathematics. Music is only created and experienced as music. Thus, there is a natural connection between mathematics and music: Both are experienced as pure objects of the brain, and both have meaning outside of the brain only by artificial connections. Back when I was teaching High School Algebra, I had a student who was gifted in music, but not so gifted with mathematics. "Give me an A" = 440hz Some basics: Music is made up of sound. There are two constant values in music. Pythagoras Scales Harmonics. Harmonic. The nodes of a vibrating string are harmonics. Two different notations of natural harmonics on the cello. First as sounded (more common), then as fingered (easier to sightread). A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency.
Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency (first harmonic) is 25 Hz, the frequencies of the next harmonics are: 50 Hz (2nd harmonic), 75 Hz (3rd harmonic), 100 Hz (4th harmonic) etc. Characteristics[edit] Harmonics and overtones[edit] An overtone is any frequency higher than the fundamental. Playing a harmonic on a string. Harmonic (mathematics) Laplace operator.
The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics, where the operator gives a constant multiple of the mass density when it is applied to a given gravitational potential. Solutions of the equation ∆f = 0, now called Laplace's equation, are the so-called harmonic functions, and represent the possible gravitational fields in free space. The Laplacian occurs in differential equations that describe many physical phenomena, such as electric and gravitational potentials, the diffusion equation for heat and fluid flow, wave propagation, and quantum mechanics.
The Laplacian represents the flux density of the gradient flow of a function. Definition[edit] The Laplace operator is a second order differential operator in the n-dimensional Euclidean space, defined as the divergence (∇·) of the gradient (∇ƒ). Where the latter notations derive from formally writing Motivation[edit] where. Pierre-Simon Laplace. Pierre-Simon, marquis de Laplace (/ləˈplɑːs/; French: [pjɛʁ simɔ̃ laplas]; 23 March 1749 – 5 March 1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics.
He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace.[2] Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming.
The Laplacian differential operator, widely used in mathematics, is also named after him. Laplace is remembered as one of the greatest scientists of all time. Early years[edit] His parents were from comfortable families. Laplace's equation. In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often written as: where ∆ = ∇2 is the Laplace operator and φ is a scalar function. In general, ∆ = ∇2 is the Laplace–Beltrami or Laplace–de Rham operator. Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations. The general theory of solutions to Laplace's equation is known as potential theory.
The solutions of Laplace's equation are the harmonic functions, which are important in many fields of science, notably the fields of electromagnetism, astronomy, and fluid dynamics, because they can be used to accurately describe the behavior of electric, gravitational, and fluid potentials. Definition[edit] In three dimensions, the problem is to find twice-differentiable real-valued functions f, of real variables x, y, and z, such that In Cartesian coordinates In cylindrical coordinates, or. Eigenvalues and eigenvectors. In this shear mapping the red arrow changes direction but the blue arrow does not.
The blue arrow is an eigenvector of this shear mapping, and since its length is unchanged its eigenvalue is 1. An eigenvector of a square matrix that, when the matrix is multiplied by , yields a constant multiple of , the multiplier being commonly denoted by . (Because this equation uses post-multiplication by , it describes a right eigenvector.) The number is called the eigenvalue of corresponding to In analytic geometry, for example, a three-element vector may be seen as an arrow in three-dimensional space starting at the origin. Is an arrow whose direction is either preserved or exactly reversed after multiplication by . Is an eigenfunction of the derivative operator " ", with eigenvalue , since its derivative is is the set of all eigenvectors with the same eigenvalue, together with the zero vector.[1] An eigenbasis for .
Eigenvalues and eigenvectors have many applications in both pure and applied mathematics. And or.