Number theory image

[matqkks]

Are there any good images that can be used as a hook for an elementary number theory course?

 

[firemath]

A particular favorite of mine is fractals. Of any kind....

 

[Romsek]

Fractals of this have nothing to do with number theory. They are a visual representation of convergence rates of non-linear differential equations.

Here's an image having to do with number theory

 

[firemath]

There is such a thing as number theory fractals.
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Also, didn't OP say "a hook?" My geometry book had a fractal on the front, and it never said a word about fractals.

 

[Steven G]

There is such a thing as number theory fractals.
.View attachment 15423
Also, didn't OP say "a hook?" My geometry book had a fractal on the front, and it never said a word about fractals.

Yes, the OP said a hook. But went on to say a hook for a number theory course!

 

[firemath]

Yes, the OP said a hook. But went on to say a hook for a number theory course!

I see. As in, "a legitimate hook"......

 

[Romsek]

There is such a thing as number theory fractals.

Number theory is about the natural numbers. That's it. Give me an example of a "number theory fractal"

The Sierpinski thing you had a pic of isn't one.

 

[firemath]

This is the best I can do.

Pathetic.

 

[firemath]

How's this?

Number theory visual from Wikipedia.
Hrm. Rather fractal-like..........

 

[Deleted member 4993]

From Quanta:

 

[Cubist]

I like the sunflower seed patterns, which link to Fibonacci numbers

 

[Deleted member 4993]

I like the sunflower seed patterns, which link to Fibonacci numbers

reference:

https://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/

 

[firemath]

Number theory is about the natural numbers. That's it. Give me an example of a "number theory fractal"

The Sierpinski thing you had a pic of isn't one.

Frac-tal (noun)

a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.

Number Theory (noun)
the branch of mathematics that deals with the properties and relationships of numbers, especially the positive integers.

Combine them, and you with have an accurate, albeit rather informal definition.

As for the "Sierpinski thing," is is from a blog that discusses the properties of Pascal's triangle and number theory in regards to the Sierpinski fractal.