Izzy says no, I say yes

compilation of my haikyuu scene drawings!!!

Botanist’s Window 🌱

Twitter | Instagram | Print shop

Literally my entire fucking life. I wish I had learned to say no like everyone else

I CHOKED

this is something

HE’S FINE!!!!!

and if you turn to ur left you’ll see the emos

is that my chemical romance?

OH MY GOD not every group of emos is my chemical romance stfu tumblr

but it actually is my chemical romance

this is the funniest fuckibg thing I’ve ever seen

I’ve…. seen this everywhere except on Tumblr itself. It’s the blessed post.

I reblog this everytime it comes on my dash and I’m unashamed

I’ve waited so long to see this post in person

Damn…… What a way 2 start the decade. Ive only seen this post in screenshots…….

YOU GUYS 

LOOK AT THIS

I’m fucking crying 

DHSGGDHDHSHS

Robert Plant at “Electric Magic,” November 1971, days after the release of Led Zeppelin IV, by Fin Costello.

oh how far you’ve come, Satan post

oh how far you’ve come

IT’S BACK

OH MY GOD IT HAS RETURNED AND IT’S LONGER THAN BEFORE!

THE ETERNAL POST

In the last Science Fact I spoke of lichens as an indicator species for air quality. Here’s more about these weird little Frankenstein blends.

Support Science Fact Friday on Patreon! Transcript below the break.

Keep reading

A deeply intuitive, aesthetically pleasing geometrical “proof without words” that the sum of the first n cubes is the square of the nth triangular number, sometimes called Nicomachus’s theorem.

A beautiful geometric visualization of positive-valued binomial expansions, the algebraic expressions produced by raising sums of variables (a, b) to natural-valued powers n. The algebraic structures and procedures of binomial expansion are described by the binomial theorem–which, in turn, is proved by the above figures. 

Given (a+b)^n, there will be (n+1)-many terms, c(a^(n-m))(b^m), where c is a constant, and a and b are variables. 

By tradition, these terms are arranged in descending order by powers of the leading term, a. Accordingly, the binomial expansion of (a+b)^n begins with the term having the highest power of a, which is a^n for all n. 

The remaining n-many terms are ordered such that the exponent of each successive a term (n-m) decreases by one. Correspondingly, the exponent of the b term (m) increases by one, such that (n-m)+m=n. 

The binomial coefficients c for each successive term c(a^(n-m))(b^m) are described by Pascal’s triangle. Given (a+b)^n, the nth row of Pascal’s triangle contains (n+1)-many numbers, which are the coefficients c, listed in the order described above.

Note that the exponent n is the dimension of the figures pictured above. This is no coincidence; the term (a+b)^n can be depicted geometrically by a figure whose measure (length, area, volume, hypervolume, etc.) is the quantity produced by multiplying (a+b), n-many times. 

Additionally, observe that the coefficients c give the quantity of n-dimensional figures required to fill in the missing bits of area, as illustrated by the figures. For example, in order to fill the volume (a+b)^3, we use two cubes of volume a^3 and b^3, and the remainder is filled by 3 “plate-like” figures and 3 “tube-like” figures (each of whose dimensions are (a^2)b and a(b^2), respectively).

Mathematics is beautiful. <3

ICONIC