Iphleandro-blog - Real

iphleandro-blog - Real
iphleandro-blog - Real

More Posts from Iphleandro-blog and Others

6 years ago
A Beautiful Geometric Visualization Of Positive-valued binomial Expansions, the Algebraic Expressions produced

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

7 years ago
A For-funsies Furry Portrait Of This Cool Dude With The Fabulous Art -> @poisondynamite / @redhotsneakers

A for-funsies furry portrait of this cool dude with the fabulous art -> @poisondynamite / @redhotsneakers <- Go check ‘em out!!!!! >w<)/

7 years ago
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch
Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch

Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch

7 years ago
David Maitland, Feltwell, United Kingdom

David Maitland, Feltwell, United Kingdom

Subject: Coral sand Technique: Brightfield Magnification: 100x

6 years ago
Zany Zebra Facts: 1) Each Zebra Has A Unique Stripe Pattern—no Two Are Alike. 2) A Zebra’s Eyesight

Zany zebra facts: 1) Each zebra has a unique stripe pattern—no two are alike. 2) A zebra’s eyesight at night is thought to be about as good as that of an owl. 3) Zebras have a pad of fat under their mane that keeps it standing straight up.

Thanks to Todd Lahman for the stunning shot of Zari the zebra.

6 years ago
Rest In Peace, Marie Severin. A Visionary Artist For Marvel And Co-creator Of #Spiderwoman, Her Work

Rest in peace, Marie Severin. A visionary artist for Marvel and co-creator of #Spiderwoman, her work shaped comics and inspired millions.

“Spiderwoman” by ayhotte: http://bit.ly/2LG2IGT  

6 years ago
Ammonite Fossil (Goniatite, Devonian) - Atlas Mtns, Morocco

Ammonite Fossil (Goniatite, Devonian) - Atlas Mtns, Morocco

6 years ago

I want to be the first person on the moon to shoot a sniper rifle at earth and hit a wasp nest.  my whole life so far is leading up to that moment

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