Glad To See Your Back. Love Your Work. As Always, Keep Up The Good Job! And Btw, Nice Covergirl Photo

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 ->

Wow, I just love when science is put to practical use!

Pun on ‘Doppler Shift’.

I love it when people take up Physics concepts and incorporate them into the realms of everyday life. 

The Doppler effect (or Doppler shift) is the change in frequency of a wave for an observer moving relative to its source. 

It is commonly observed in sound. When a car is approaching you, the pitch (frequency) of the car increases and when it recedes, the pitch decreases. right? This is the Doppler Shift in action. 

Or to put it in TBBT verbatim - “ Neeeeoooowwwww!”

The Doppler Shift works with light exactly the same as with sound! Just as sound seems higher or lower in pitch as the object is moving towards or away from you, light appears higher in frequency (color) when the object is moving towards you, and lower in frequency/color when moving away from you. The order of colors/frequency of light that we can see is: 

Lower Frequency               Higher Frequency

red - orange - yellow  - green - blue - violet

So a far away object moving quickly away from you would appear more reddish than if it were standing still. The same object moving quickly towards you would appear more bluish than if it were standing still.

PC : Dean Johnson

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.

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

Would like a map of the whole area, just to know for sure i’ve been to all the places :)

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!

Geometry apps!

I have stumble upon some of the neatest apps, for a person like me that love geometry, these apps are just what I’ve been looking for!

Euclidea:

IOS: https://itunes.apple.com/app/id927914361 Android: https://play.google.com/store/apps/details?id=com.hil_hk.euclidea This app is only Euclidean geometry, that’s what I like the most. Appinfo: Euclidea is a brilliantly original way to learn about, explore and have fun with Euclidian Constructions! Your task is to solve interesting challenges by building geometric constructions with a straightedge and compass. If you design the most elegantly simple solutions in the least number of moves, you’ll earn the highest scores. Solutions are scored in lines (L) and elementary Euclidean constructions (E).

XSection:

IOS: https://itunes.apple.com/us/app/xsection/id1069933287?mt=8 Haven’t found it on Android yet, but this app aims to learn you about Polyhedrons, cross sections and geometry. Appinfo: Learn how to construct cross sections of polyhedrons. Study different techniques, train yourself, and then solve geometric puzzles. 

Pythagorea:

IOS: https://itunes.apple.com/us/app/pythagorea-geometry-on-square/id994864779?mt=8 Android: https://play.google.com/store/apps/details?id=com.hil_hk.pythagorea&hl=sv Just found this game, so I paste the appinfo: Pythagorea is a collection of geometric puzzles of different kind that can be solved without complex constructions or calculations. All objects are drawn on a grid whose cells are squares. A lot of levels can be solved using just your geometric intuition or by finding natural laws, regularity, and symmetry. 

Pythagorea60:

IOS: https://itunes.apple.com/us/app/pythagorea-60-geometry-on/id1043064990?mt=8 Android: https://play.google.com/store/apps/details?id=com.hil_hk.pythagorea60&hl=sv Just found this game, so I paste the appinfo: Pythagorea 60° is a collection of more than 270 geometric problems of different kind that can be solved without complex constructions or calculations. All objects are drawn on a grid whose cells are equilateral triangles. A lot of levels can be solved using just your geometric intuition or by finding natural laws, regularity, and symmetry. 

Horis International Limited

All these games are made from the same developer, Horis International Limited:  IOS: https://itunes.apple.com/us/developer/horis-international-limited/id646324304 Android: https://play.google.com/store/apps/developer?id=HORIS+INTERNATIONAL+LIMITED Big up, love this!

Wow, “ For a photon, its entire existence is instantaneous. “ , that put things in perspective! 

Ask Ethan #109: How do photons experience time?

“[L]ight takes about 8 minutes to travel from the sun to earth. Light travels at the speed of light. If you do that relativity kicks in. So my question is, how much time passes for the photons traveling? In other words, how much have the photons aged when the reach the earth? Thanks for considering this.”

Travel at any constant speed, at rest, slowly, or near the speed of light, and you’ll experience time passing at the same rate it always does: one second per second. If someone else is moving relative to you, they’ll see your clock run slow (and you’ll see theirs run slow) depending on how quickly you move relative to one another. But what about a photon, which moves at the speed of light? From your point of view, no matter what your motion is, you won’t see time pass for it at all, and it won’t even experience time! For a photon, its entire existence is instantaneous.

This somehow reminds me of: http://www.derekhugger.com/merlot.html Hope you like it.

Breathe.