# Category Archives: mathematics

## Geometric Algebra (1)

Geometric algebra is not to be confused with algebraic geometry. Geometric algebra is also known as Clifford algebra which has many applications in physics and engineering. Algebraic geometry, on the other hand, is a branch of abstract mathematics. Geometric algebra … Continue reading

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## Geometric interpretation of sqrt(-1)

I wrote a post titled Euler rule is almost mystical where I mentioned the Cotes-Euler identity Euler rule is a special case of the Cotes-Euler identity. represents the rotations of the complex unit vector. This provides a natural interpretation for … Continue reading

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## Biquaternion

In the previous post we have seen that a quaternion is defined as where and , , , are real numbers. Biquaternion The biquaternion is a complexified quaternion where , , , are complex numbers. The basis elements , , … Continue reading

## Quaternion

Quaternions are 4-dimensional generalizations of complex numbers. It can also be said that the basis elements , , of a quaternion are 3-dimensional generalization of the pure imaginary number . William Rowan Hamilton discovered quaternions in 1843. After many years … Continue reading

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## Mathematical Spirals

The equations of the basic spirals are given in polar coordinates. The is the radius and is the angle measured from the positive horizontal axis.The and are constants. Archimedes Spiral http://mathworld.wolfram.com/ArchimedesSpiral.html Fermat Spiral http://mathworld.wolfram.com/FermatsSpiral.html Logarithmic Spiral http://mathworld.wolfram.com/LogarithmicSpiral.html Golden Spiral The … Continue reading

## Golden Number and Lucas Sequence

The golden number is . There is extensive literature on the golden number which is also known as the golden ratio. The exposition in Wolfram Mathworld [http://mathworld.wolfram.com/GoldenRatio.html] is excellent. John Baez gave an interesting exposition [http://math.ucr.edu/home/baez/week203.html]. Mario Livio’s book “The Golden … Continue reading

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## Phase enables relativity

Physicists are experts at assigning new meanings to the terms established in common language. I mentioned the term “dual” or “duality” before. In common language dual means two. In physics dual means equivalent. Physicists use the word “phase” in different … Continue reading

Posted in geometry, mathematics, physics, science, tutorial

## Euler rule is almost mystical

In his wonderful book “Road to Reality” Roger Penrose mentions that the Euler rule is “almost mystical” because it relates the 5 fundamental numbers 0, 1, i, π and e to each other. The Euler rule is a special case … Continue reading

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## i raised to the power of i

Remember the general rule ab  = e(a ln(b)) Using this rule we can compute i raised to the power of i ii = e(i ln(i)) = e(i πi/2) = e(-π/2) = 0.207879576…. remember that ln(1)=0 ln(i)= iπ/2 and

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## Zero

Symbols for zero appeared in many cultures Before Common Era (BCE). The philosophical conception of zero, however, is usually attributed to the Indian philosophy. The evidence is in the Sanskrit language. The Sanskrit word “shunya” meaning “emptiness” or “void” was … Continue reading

Posted in history, mathematics, philosophy |

## Essays by Suresh Emre

A new synthesis of Spiritual Philosophy is presented in Definitions and Summary of Soul Monism I volunteer for the Renaissance Universal (RU) movement. A Vision for a Universal Renaissance. The complete list of my articles is given in http://sureshemre.wordpress.com/index/

## Super Modeler Function

Data modeling capabilities of this function is limitless. X is a continous variable. S, R, T are constants. By changing the constants see how the Super Modeler Function is behaving. In the graphs below the horizontal axis is the X … Continue reading

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