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Thread: High tech maths!

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    Brett Nortje's Avatar Senior Member
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    High tech maths!

    I was wandering around the wikipedia today, and all of a sudden, a thing called analysis caught my eye. naturally, i wanted to investigate.

    The foundations of this are to find the identity of indiscernibles, the symmetry and triangle inequality. to find these values, you need to show that d[xy] equals or is greater than zero. so, this finds positive numbers.

    Now, to find the indiscernaibles, you need to find that x = 0 and d = 0 and if that is true, y equals zero. this is indiscernibles, which means all the negative angles will add up to zero, or, be reduced from their negative places to zero.

    Then, you need to observe that [x] = [y], or, that swapping [x] with y will equal the same thing.

    Then, you need to observe that [z] and [x] are greater than [y].
    !! Thug LIfe !!

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    But, this is not simple enough, so we need to simplify it further, yes?

    If you were to observe that [z] and [x] are greater than [y], and, that multiplying [x] by [y] will yield the same number, no matter which way round you multiply them, then you will also see that [y] = 0 and that [x] must equal a positive number that needs to equal zero, so, [x] is the opposite to [z], as if minus 5.3 and 5.3.
    !! Thug LIfe !!

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    I've been helping my son with his math lately, fractions. He taught me something new, forgot the term for it now.

    Subtracting fractions: 4 and 1/4 minus 3 and 3/4

    You add the fractions and put that number on the top, take one from the whole number and re-establish the denominator and there it is, so it then becomes: 3 and 5/4 minus 3 and 3/4 - answer being 2/4 or 1/2.
    my junk is ugly

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    Geometry of 'curves.'

    When it comes to this, it can be painful to measure. if you do not have the necessary equipment, you can use ruler to find the angles.

    All you have to do is extend the lines along the lines, and then see how many degrees they are. this will make it easier in the end, i promise!

    So, you take your right angle on the page you have, naturally drawn there, then you find the amount of numbers to find the right angle, half that for a acute right angle, and find the ratio where it becomes forty five degrees. then, you count how many units it is for a right angle of the curved line, naturally, and then you know the ratio. then, you take the ratio and divide logically.

    Now, when you have to find the meeting points of two or three curved lines, you can just measure!
    !! Thug LIfe !!

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    Critical path method.

    This is said to be a sub field of mathematics. i have borrowed an example from wikipedia for my illustration of this type of maths.

    Criticalpathmethod.svg.png

    Quote Originally Posted by http://en.wikipedia.org/wiki/Critical_path_method
    The essential technique for using CPM [6][7] is to construct a model of the project that includes the following:
    1. A list of all activities required to complete the project (typically categorized within a work breakdown structure),
    2. The time (duration) that each activity will take to complete,
    3. The dependencies between the activities and,
    4. Logical end points such as milestones or deliverable items.
    Like said in the picture.

    Now, if you were to observe that certain activities should take preference, the chart should start in the center and work around in a circle, like a spiral. this will make it easier to connect things, yes? then you can make emergency plans where you adjust the placement of the little spheres and then make them reorganize themselves like a touch screen graph of today.
    !! Thug LIfe !!

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    Differential equations.

    Quote Originally Posted by http://en.wikipedia.org/wiki/Differential_equation
    A differential equation is a mathematicalequation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering,physics, economics, and biology.In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form.
    If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.
    So, you find the equation is usually a lot of powers and symbols with a lot of quadratic equations, yes? this would be simplest solve by flipping them around as we are taught with quadratic equations, and, then rubbing out the power numbers we find similar. this simplifies it, yes?

    Then, it is algebra! this can be solved by applying numbers for the symbols and using a scientific calculator, of course.
    !! Thug LIfe !!

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    Quadratic equations made easier.

    This is where you have about four sums separated into two or more sections with division lines splitting them into a total of at least four sums. to work this out easier, you need to multiply the things that are divided, then switch them to negative numbers, then add them as if they were coming to be positive numbers.
    !! Thug LIfe !!

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    Logarithms.

    In mathematics, the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 10 to the power 3 is 1000: 1000 = 10 × 10 × 10 = 103.More generally, for any two real numbersb and x where b is positive and b ≠ 1,The logarithm to base 10 (b = 10) is called the common logarithm and has many applications in science and engineering. Thenatural logarithm has the irrational (transcendental) number e (≈ 2.718) as its base; its use is widespread in mathematics, especially calculus. The binary logarithm uses base 2 (b = 2) and is prominent in computer science.
    Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors:
    provided that b, x and y are all positive and b ≠ 1. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century.
    Logarithmic scales reduce wide-ranging quantities to smaller scopes. For example, the decibel is a unit quantifying signal power log-ratios and amplitude log-ratios (of which sound pressure is a common example). In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals. They describe musical intervals, appear in formulae counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting.
    In the same way as the logarithm reverses exponentiation, the complex logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant; it has uses in public-key cryptography.
    To find the values here, you need to find the values of everything else that you can, then you divide them by themselves - reverse of square - and then you have the total of the logarithm.
    !! Thug LIfe !!

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    Parabola.

    Quote Originally Posted by http://en.wikipedia.org/wiki/Parabola
    A parabola (/pəˈrćbələ/; plural parabolas or parabolae, adjective parabolic, from Greek: παραβολή) is a two-dimensional, mirror-symmetricalcurve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape.One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that areequidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a planewhich is parallel to another plane which is tangential to the conical surface.[a] A third description is algebraic. A parabola is a graph of a quadratic function, such as
    The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point on the axis of symmetry that intersects the parabola is called the "vertex", and it is the point where the curvature is greatest. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola which is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are geometricallysimilar.
    Parabolas have the property that, if they are made of material that reflects light, then light which enters a parabola travelling parallel to its axis of symmetry is reflected to its focus, regardless of where on the parabola the reflection occurs. Conversely, light that originates from a point source at the focus is reflected into a parallel ("collimated") beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other forms of energy. This reflective property is the basis of many practical uses of parabolas.
    The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas.
    Strictly, the adjective parabolic should be applied only to things that are shaped as a parabola, which is a two-dimensional shape. However, as shown in the last paragraph, the same adjective is commonly used for three-dimensional objects, such as parabolic reflectors, which are really paraboloids. Sometimes, the noun parabola is also used to refer to these objects. Though not perfectly correct, this usage is generally understood.
    180px-Conic_Sections.svg.png

    This is like a bit of area and radius from geometry. basically, you can find the values you need by making a bigger circle inside the 'cone' by doubling the cone so that it comes out both sides. so, instead of having one cone, you have two cones, one joined at the end of the other, like a triangle within a triangle, or like two matches joined on the wooden side to become a double flint ended match, yes?

    This will make the whole working out of the parabola much easier, as, you will be dealing with radius inside the cones.
    !! Thug LIfe !!

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    Finding the degrees inside the circle will be made easier if you were to reverse the circles so that there is two 'circles' instead of just one, and, then finding the degrees of the 'vertical' circle by finding a few points close to the 'cone.'
    !! Thug LIfe !!

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