Animal Gaits For Animators By Stephen Cunnane

Wow! You have come real far with this now! Amazing work. Keep it up!

Mechanics of Form. Work in progress.

Master of geogebra helped me out with this! Thanks!

Table Saw

@mrvmt requested a table saw sketch, and this is the first draft. In GeoGebra here.

Wow, this is the coolest comic i ever read! Got your book (”What if?”) and now think its the second coolest thing i read! :) Keep it up!

Hey IBM,  Always loved your posts. BUT THIS, you want people to drink milk from a cow? The milk is for the calf! Shame on you for spreading the lie that milk is good for the body. It’s proven that milk is not good for humans after the age of 12. Stop treat animals like they are made for us humans to abuse! There is no humane way to kill or inseminate another living creature! Hope this is your first and last post propagates for animal abuse!

Dairy DNA

Milk, it does a body good, and we want to make sure it stays that way. In order to help protect the safety of this ingredient found in so many foods, IBM and Cornell University are working on a way to monitor raw milk straight from the source. By sequencing the DNA and RNA of milk and its surrounding microbes, they hope to be able to instantly detect food safety hazards so they don’t have a chance to make it into your glass or onto your plate.

Learn more ->

Just the ruler missing. Love to draw with those tools!

Beautiful, where can I get my hands on one of these? :) 

Dragon Fractal - Level 5

If you take each of the 4 sides of a square and modify the angle of the dragon fractal as you go up, you get this shape. I’m still fighting the 3d models to get a nice smooth version.

Back when I was in school, this concept was really hard for me to grasp my head around, and I must say, this was a compelling way to understand the function of multiplying with negative numbers!

Thanks!

By virtue of everyday usage, the fact that (-1) x (-1) = 1 has been engraved onto our heads. But, only recently did I actually sit down to explore why, in general negative times negative yields a positive number !

Intuition.

Let’s play a game called “continue the pattern”. You would be surprised, how intuitive the results are:

2 x 3 = 6

2 x 2 = 4

2 x 1 = 2

2 x 0 = 0

2 x (-1) = ??  (Answer : -2 )

2 x (-2 ) = ?? (Answer : -4 )

2 x ( -3) = ?? (Answer : -6 )

The number on the right-hand side keeps decreasing by 2 !

Therefore positive x negative = negative. 

2 x -3 = -6

1 x -3 = -3

0 x -3 = 0

-1 x -3 = ?? (Answer : 3)

-2 x -3 = ?? (Answer : 6)

The number on the right-hand side keeps increasing by 3.

Therefore negative x negative = positive.

Pretty Awesome, right? But, let’s up the ante and compliment our intuition.

The Number Line Approach.

Imagine a number line on which you walk. Multiplying x*y is taking x steps, each of size y.

Negative steps require you to face the negative end of the line before you start walking and negative step sizes are backward (i.e., heel first) steps.

So, -x*-y means to stand on zero, face in the negative direction, and then take x backward steps, each of size y.

Ergo, -1 x -1 means to stand on 0, face in the negative direction, and then take 1 backward step. This lands us smack right on +1 !

The Complex Numbers Approach.

The “i” in a complex number is an Instruction! An instruction to turn 90 degrees in the counterclockwise direction. Then i * i would be an instruction to turn 180 degrees. ( i x i = -1 ). where i = √-1

Similarly ( -1 ) x i x i = (- 1 ) x ( -1 )= 1. A complete revolution renders you back to +1.

We can snug in conveniently with the knowledge of complex numbers. But, complex numbers were established only in the 16th century and the fact that negative time negative yields a positive number was well established before that.

Concluding remarks.

Hope you enjoyed the post and Pardon me if you found this to be rudimentary for your taste. This post was inspired by Joseph H. Silverman’s Book - A friendly Introduction to Number Theory. If you are passionate about numbers or math, in general it is a must read.

There are several other arithmetic methods that prove the same, if you are interested feel free to explore.

Have a Good Day!

PC: mathisfun

Greenpeace #clickclean campaign GIFs ‘Wind Turbine Likes’

Oh, so your from Denmark then, or maybe its “Skåne” ? :)

Welcome to my world of dyslexia... :)

When I'm halfway through a sentence and suddenly realise there is no way out of the grammatical crater I have dug myself