Visualizing Math

A blog dedicated to mathematics. 

 
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backwardinduction:

In mathematics, an algebraic set is the set of solutions of a system of polynomial equations. Algebraic sets are sometimes also called algebraic varieties, but normally an algebraic variety is an irreducible algebraic set, i.e. one which is not the union of two other algebraic sets. Algebraic sets and algebraic varieties are the central objects of study in algebraic geometry. The word “variety” is employed in the sense which is similar to that of manifold; the difference is that a variety may have singular points, while a manifold may not. In the Romance languages, both varieties and manifolds are named by the same word, a cognate of the word “variety”.

Proven around the year 1800, the fundamental theorem of algebra establishes a link between algebra and geometry by showing that a monic polynomial in one variable with complex coefficients (an algebraic object) is determined by the set of its roots (a geometric object). Generalizing this result, Hilbert’s Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings and algebraic sets. Using the Nullstellensatz and related results, mathematicians have established a strong correspondence between questions on algebraic sets and questions of ring theory. This correspondence is the specifity of algebraic geometry among the other subareas of geometry.

The Twisted Cubic, pictured above, is an algebraic variety.

[Source: http://en.wikipedia.org/wiki/Algebraic_variety]

allofthemath:

This, ladies and gentlemen and genderqueer folks, is Pascal’s tetrahedron, a three dimensional analogue of Pascal’s triangle, and it’s pretty freaking great.

I’ve never heard of this before!

(via mathematica)

tigburr:

coolmathstuff:

allofthemath:

appliedmathemagics:

themathkid:

Can’t. Stop. Watching.

this is hypnotic…

Conic sections are all connected! A hyperbola is an anti circle, in this case.

Remember, the equation for a circle involves adding x squared and y squared, while the equation for a hyperbola involves subtracting one from the other. The other consequence of this is that is that if you extend the graph of either one to include imaginary and complex x or y values, a hyperbola contains a circle in its empty space, and a circle has a hyperbola surrounding it.

I FOUND THE MATHEMATICIANS!
FRIENDS! FRIENDS!!

tigburr:

coolmathstuff:

allofthemath:

appliedmathemagics:

themathkid:

Can’t. Stop. Watching.

this is hypnotic…

Conic sections are all connected! A hyperbola is an anti circle, in this case.

Remember, the equation for a circle involves adding x squared and y squared, while the equation for a hyperbola involves subtracting one from the other. The other consequence of this is that is that if you extend the graph of either one to include imaginary and complex x or y values, a hyperbola contains a circle in its empty space, and a circle has a hyperbola surrounding it.

I FOUND THE MATHEMATICIANS!

FRIENDS! FRIENDS!!

(via imathematicus)

cherry-merchant:

Sierpinski transformation

centerofmath:

The Ulam spiral shows a pattern in the (unpredictable) primes

(via mathmajik)

mathani:

Get you best paper, cut a circle and fold it, fold it so that the circumference falls on a fixed point inside. Repeat, using random folds. Now see the creases. This is how you paper-fold an ellipse.

mathani:

Get you best paper, cut a circle and fold it, fold it so that the circumference falls on a fixed point inside. Repeat, using random folds. Now see the creases. This is how you paper-fold an ellipse.

(via try-and-touch-my-asymptote)

hipster-graphs:

1: sinx=cosy

2: 2siny=cosx

3: sinx=cosy+1

4: sinx=cosy+2

5: sinx=cosy+1

Asker Anonymous Asks:
I'm not very good at math, and I don't really understand very much of what you post, BUT I LOVE IT!!
visualizingmath visualizingmath Said:

We have a lot in common, Anonymous. Thanks for the message! 

Asker Anonymous Asks:
I just love your blog! So intersting! :D
visualizingmath visualizingmath Said:

Thanks, Anonymous!

Asker Anonymous Asks:
This blog is awesome! Definitely one of my favorites. I love learning maths, and what you post makes maths look even more interesting!
visualizingmath visualizingmath Said:

Thank you! I’m glad you love to learn mathematics! 

mindfuckmath:

Seeing as how it’s Oscar Sunday, here is an awesome math flavoured movie quiz from Spiked Math.  You can find the solutions here, and if you enjoy this quiz you’ll enjoy Part 2 and Part 3.  For the record, I’m predicting that 12 Years a Slave collects a whole lot of richly deserved Oscar love including Best Picture.