#alternating

[instigatorjosten]

dont let me alone in a room w jean moreau, its gonna get wet in there

[liy-u]

⠀⠀⠀⠀⠀⠀⠀⠀⠀✿⠀　┊　⠀⌑⠀⠀⠀🐈

[rvexillology]

American flag with Red, White, and Blue alternating stripes

from /r/vexillology Top comment: Reminds me of Capt. John Paul Jones Serapis Flag https://en.m.wikipedia.org/wiki/Serapis_flag

[usgsbiml]

Collected by one "E.P. Reed" probably about 100 years ago in Central Chile this is from an orphaned collection of bees from the Smithsonian.  While in the process of returning we are taking a few pictures of some of the more interesting bees.  This is Caupolicana fulvicollis.  At least some, if not all, of these bees are crepsucular bees...out only at dawn or at dusk where they have a secret pollen handshake with the few plants that only open their blossoms in crepusculance (possibly not a real word, but sounds like it should be to me).  Note the large ocelli on this bee....a pretty good sign that it indeed is working in low light.  Picture by Anders Croft from our lab.

[numb3rth30ry]

An exceedingly clever visualization of a Cauchy Product. 

The first leap of creativity is choosing to represent quantities as black and red squares. Each black square has value 1, each red square has value -1.

The checkerboard is constructed by expanding both series to be multiplied. Each series is written term-wise along the edge of a grid. I.e., one expanded series is written vertically, left of the rows, and the other is written horizontally, above the columns. Each row (or column, cell, etc.) can be obtained by multiplying the corresponding values along the rows and columns.

For example: the upper-left corner cell represents (1)x(1)=1, a black square. The cell to its right (in the same row) represents (1)x(-1)=-1, a red square. The pattern alternates accordingly. 

Observe how all the squares along the diagonal, from the corner, are also black. This is because they represent products of matching signs (both positive or negative), and are thus always positive. For similar reasons, all diagonals (and anti-diagonals) have the same color.

The checkerboard represents the left-hand side of the Cauchy product--it is obtained by multiplying two series. The right hand side of the Cauchy product, a single, new series, is represented by the pyramidal structure pointed to by the arrow.

The pyramid is made by reorganizing the checkerboard. To see how, imagine isolating each anti-diagonal. Beginning with the smallest anti-diagonals and working outward, rotate the square(s) and add them together, so they fit side by side (making rectangles). Layer the rectangles top to bottom from smallest to largest. 

Since successive diagonals alternate in sign (positive/negative), we obtain a pyramid of alternating black and red layers. Each layer has one more square than the previous. Recalling that black squares are positive 1′s and reds are negative, we can convert the layers of the pyramid into individual terms of an alternating series

which is the right-hand side of the Cauchy product. Incredible!

Mathematics is beautiful. <3

[earthstory]

These swirling clouds captured by NASA’s Terra Satellite are known as Von Karman vortices. They are created when a mass of fluid, such as water or air, encounters an obstacle and creates swirls going in alternating directions. The obstacle in this instance is Isla Socorro, a volcanic island in the Pacific Ocean. The island, which is located a few hundred kilometers off the west coast of Mexico and the southern tip of Baja California, is part of the Revillagigedo Archipelago. Jean Photograph: MODIS/Terra/NASA

[renaissanceswordclub]

#flow #drill with #students keeping #moving while #alternating #attacks #sword #historicalfencing #training💪 #destreza #rapier #dagger #martialarts #sportlife #fitnesslife #surrey (at Frimley Community) https://www.instagram.com/p/BswM5ucnaft/?utm_source=ig_tumblr_share&igshid=1i0ad8vpi4bsw