fouriestseries:

Curves of Constant Width and Odd-Sided Reuleaux Polygons

A curve of constant width is a convex, two-dimensional shape that, when rotated inside a square, always makes contact with all four sides.

A circle is the most obvious (but somewhat trivial) example. Some non-trivial examples are the odd-sided Reuleaux polygons — the first four of which are shown above.

Since they don’t have fixed axes of rotation, curves of constant width (except the circle) have few practical applications. One notable use of the Reuleaux triangle, though, is in drilling holes in the shape of a slightly rounded square (watch one of the triangle’s vertices and notice the shape it traces out as it spins).

On a less technical note, all curves of constant width are solutions to the brainteaser, “Other than a circle, what shape can you make a manhole cover such that it can’t fall through the hole it covers?”

Mathematica code posted here.

Additional source not linked above.

(via spring-of-mathematics)

drivojunior:

This is a sin

Lets see how many followers i lose with this one :)

drivojunior:

This is a sin

Lets see how many followers i lose with this one :)

(Fonte: synapse-break, via minene-uryu)

I need a letter different from r… r’ for instance.

Analysis professor (via mathprofessorquotes)

If you’re the smartest person in the room, you’re in the wrong room

Unknown (via mofobian)

Corollary: any room with population > 0 has at least one person who should not be in it. 

Corollary: by induction, everyone in a room is n (where n is their in-room intelligence ranking) corrections from being in the wrong room. 

(via antinegationism)

(Fonte: metalhearted, via mathematica)

wibblywobbly-timeywimey-nonsense:

Teacher of the Year goes to my Statistics teacher.

wibblywobbly-timeywimey-nonsense:

Teacher of the Year goes to my Statistics teacher.

(Fonte: flyingmatthew)

hlchapman:

Love this!

hlchapman:

Love this!

amiagoodperson:

cantor dust - with fancy linear interpolation

amiagoodperson:

cantor dust - with fancy linear interpolation

spring-of-mathematics:

Happy Number

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers. More formally, given a number n = n_0, define a sequence n_1, n_2,… where n_(i+1) is the sum of the squares of the digits of n_i. Then n is happy if and only if there exists i such that n_i = 1. If a number is happy, then all members of its sequence are happy; if a number is unhappy, all members of the sequence are unhappy.
Especially, the happiness of a number is unaffected by rearranging the digits, and by inserting or removing any number of zeros anywhere in the number. For example, 19 is happy, as the associated sequence is:
    1^2 + 9^2 = 82
    8^2 + 2^2 = 68
    6^2 + 8^2 = 100
    1^2 + 0^2 + 0^2 = 1.
There are infinitely many happy numbers and infinitely many unhappy numbers. Consider the following proof: 1 is a happy number, and for every n, 10n is happy since its sum is 1, and for every n, 2 × 10n is unhappy since its sum is 4 and 4 is an unhappy number.

Maybe, “Happy Number” is a relative concept, but definitely they are interesting numbers.
See more:  Happy numbers and Happy primes at Wikipedia - Image: One by Paul Thurlby.