Xah Math Blog Archive 2013-10 to 2013-10

Equiangular Spiral, also known as log spiral, has the property that the angle of tangent to center is constant.

equi spiral def
A example of equiangular spiral with angle 80°.

Mathematician Jacob Bernoulli (1654 to 1705) requested this spiral be engraved on his tombstone with the epitaph:

Though changed I rise unchanged

more pics and properties at Equiangular Spiral

have you ever heard people say “i am never good at math…”?

hi, am a mathematician. When the subject of math comes up in conversation, the usual response i get is a somewhat uneasy utterance of “i am never good at math”.

you know what? that's right, you are a idiot, period.


Mathematica 7 deltoid notebook Xah 2013-10-22
Mathematica 7 notebook, deltoid

Math Terminology: Magma vs Groupoid

The term magma for this kind of structure was introduced by Nicolas Bourbaki. The term groupoid is an older, but still commonly used alternative which was introduced by Øystein Ore.

why did the Bourbaki guys introduce the term magma? it seems to me groupoid is a better term. Was it introduced to avoid confusion due to the many slightly different definitions of groupoid?

Why is Sine Called Circular Function

this is why sine, cosine, are called circular functions


all the trig function, {sin, cos, tan, asin, acos, atan}, can be defined using just one of them, sin.

so, there is really just one function: sine.

you can see why it's so important in math, because the nature of it is that it's the height when you sweep a circle with constant speed.

in other words, anything that rotates in a constant speed, sine is in it.

earth rotates, moon rotates, so came sine. Then, wheels are invented, more sine.

read more at Sine Curve

added the complete list. Refresh page. Math Font, Unicode, Gothic Letters, Double Struck, 𝔄 𝔅 ℭ, 𝔸 𝔹 ℂ

math gothic font. Can you identify the following letters? 𝔅 𝔙

On the Naming of Eigenvector and the Igon Value Problem

the Nature of Linear Transformation


What's Eigenvalues and Eigenvectors

math demystification: If you hear “stochastic process”, you can safely replace it with “random process”

57color coded

Algorithmic Mathematical Art

The gist here is to distill a math art into its algorithmic essence. By recursion or some encoding (such as math equation)

Hilbert curve
Space-Filling Curve
clock secondhand gear mechanism
clock secondhand gear mechanism

my concern in life is math and women. But since they are both difficult, my activity is mostly reduced to visualization aspect.

a Riemann surface. From http://3d-xplormath.org/

What is Riemann Surface? Understanding the Concept Without Math.

Wikipedia Reading Snippets: Understanding Category Theory

Category theory

In many fields of mathematics, morphism refers to a structure-preserving mapping from one mathematical structure to another. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in topology, continuous functions, and so on.

In category theory, morphism is a broadly similar idea, but somewhat more abstract: the mathematical objects involved need not be sets, and the relationship between them may be something more general than a map.

The study of morphisms and of the structures (called objects) over which they are defined, is central to category theory. Much of the terminology of morphisms, as well as the intuition underlying them, comes from concrete categories, where the objects are simply sets with some additional structure, and morphisms are structure-preserving functions. In category theory, morphisms are sometimes also called arrows.

The Importance of Terminology's Quality In Computer Languages

Math Writing Style: Use of the Term “Linear Operator” vs “Linear Function”

What is Quadratic Form in Math?

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