Tau and equality

Periodically, on June 28th, I draw attention to Tau Day, a concept in math which helps "round" out learning angles and waves. Only two days ago on June 26th, another date worth remembering occured: the Supreme Court of the United States of America has "held that state recognition of same-sex marriage is a constitutional right under the Fourteenth Amendment" [Wikipedia: "Obergefell v. Hodges"]. While I, personally, am unaffected by this decision, I do think it's an important advance in equality in the USA and I'm glad this country has chosen to see the LGBT community as I always have: equal and able to pursue what they love.



Coupled with this landmark court decision, I think we should recognize the mathematical unity of the circle of hands being joined around the United States of America these last few days. Earlier this year the "Ultimate [Half Tau] Day" (aka Pi Day) occurred and in my writing I drew attention again to how using Tau can help people understand circles, angles, and waves with ease.

Here's an entertaining overview of Tau by DNews:

URL: https://youtu.be/kmnogV9S7b8

Additionally, I invite you to watch the long version of the Tau Manifesto talk below or you can take a smaller slice of the pie by jumping back to the Half Tau article to watch the short version. Either way, let's remember the significance of June 26th as we move forward as a country and the significance of June 28th as we attempt new mathematical understanding. Through both politics and math we will find new ways to overcome obstacles and inequality both in human rights and in math education.


URL: http://youtu.be/H69YH5TnNXI

Read more about Tau here: http://www.tauday.com/

Happy Ultimate Half Tau Day!

Pi is nice, but Tau is better!


Image from "The Tau Manifesto"

Over the years, I've written about Pi and Tau. Today is the Ultimate Pi Day; March 14, 2015. And throughout the world at 9:26:53 local time, people can celebrate Pi to nine digits. Still, Pi is only one "slice" of the whole pie. Tau is the answer to learning about circles, angles, and waves in an easy and fun way. So, enjoy your slice of Pi today, but remember to give Tau's simplicity a "turn" too.


URL: https://www.youtube.com/watch?v=2hhjsSN-AiU

Read more about Tau here: http://www.tauday.com/

Getting a full slice of pie

Last year, I presented some information about the mathematical concept of "tau". Most importantly, I encouraged an educational focus toward the practical:

Keeping the students as the priority, certain "weird math" gets discarded. For example, did you know that a full pi radian angle is only 180°. If I were to use only pi to cut you a slice of pie that means you would only get half of what you asked for because a circle is really 2π. Using τ you would have access to the full 360°.

Today is again Tau Day and I would like to remind you to get that full slice of pie in your life. Use an open mind and the power of critical thinking to find the methods which expand your world-view.

As I've said in some fashion in other articles:

Never accept "because I said so"; find a better source, one which will help nurture your curiosity not belittle it. Explore the world around you, excite your mind with interest, accept the dynamic nature of "fact", and wonder at the beauty of information.

Vi has put together another fun video [YouTube] about Tau this year. As she says in the silly fun of her song:

"We get further from truth when we obscure what we say."

Tau is a simple and easy way to understand the math of circles. And, let's be honest, math is far to important to be overlooked because someone long ago decided to make it appear harder to conceptualize than it really is.

Remember, Pi is a lie!

Happy Half Tau Day!

Remember, Pi is a lie and Tau is twice the fun!

As you go about your mathematically similar day, read up on the origins and uses of Pi and Tau in those previous articles.

Goofy physics

Source: "Goofy" - Wikipedia

For years, I've pondered a question presented by Goofy in the film "A Goofy Movie" [IMDB]:

"How many cups of sugar does it take to get to the Moon?"

Having just watching the film with my kids tonight, I decided to finally calculate the answer.
Disregarding the effects of atmospheric drag and the gravity of the Sun, I can focus solely on the physics involving the gravity of the Earth and Moon ["Escape velocity" - Wikipedia]:

- A "cup of sugar" has the potential to release 3.18 MJ of energy
- The velocity required to break free of Earth (V_e^E) is 11.2 km/s
- The velocity gained by an object falling to the Moon (V_e^M) is 2.4 km/s
- My mass (Mⁱ) is approximately 77 kg ¹

Using an understanding of (simplified) rocket science [minutephysics - YouTube], we can learn the basic equation needed to calculate how much energy is needed to travel to the Moon:

Energy in Joules = (.5*Mⁱ)*((V_e^E)²-(V_e^M)²)
(38.5)*(11.2²-2.4²) = 4.61x10⁹ J = 4610 MJ

Now we know that I, as some sort of bizarre human-rocket, would need 4610 MJ of energy to travel to the Moon. We already found that 3.18 MJ of energy is in each cup of sugar.

4610 MJ / 3.18 MJ = 1450

This means that it would require the energy of 1450 cups of sugar for me to travel to the Moon. Don't worry, the hard part will be figuring out how I can fly.

---

¹ As a point of reference, the Saturn V rocket which launched Apollo 11 was 3,039,000 kg [Saturn V - Wikipedia].

Happy Tau Day

Three months and fourteen days ago, I wrote an article in celebration of "Half Tau Day" (better known to many as "Pi Day"). In that article I began to point out the benefits of using Tau (τ) or 2*pi (2π) in Mathematics.

Today, in full celebration of Tau Day, I would like to present more about the benefits of adjusting our established norms for a more comfortable digestion of Math. (A great deal of the information I will present here is processed from "The Tau Manifesto" website. I encourage you to take a more detailed look at the information there, if what I present here intrigues you.)

The constant of 2π is wide-spread in use throughout Mathematics, especially in Trigonometry and Calculus. This commonality occurs simply because of the relationship between circles and their radii.

Pi (π) exists because it is the ratio between a circle's diameter and its circumference. It has been stated (and sometimes argued) that "it is easier to measure a circle by its diameter than its radius". That may be so, but most formulas involving circles use its radius (e.g. area, angles, fractions, etc.); some charts and real world applications use radius as well, such as "pie graphs" and even slice the real-world application of slicing a piece of pie. Which means that the diameter would have to be divided after measurement anyway, especially if you want to measure more than circumference.

So, why not use a variable based on the ratio between a circle's radius and its circumference in the first place?

Circumference:

C = τ r

Area:

A = (τ/2) r²

Volume (of a sphere):

V = 2/3 τ r³

There may be some formulas which may seem more useful with π. Personally, I have no objection. Afterall, a meter is just 100 centimeters, yet we choose to use both "m" and "cm" everyday. I think π and τ should coexist in Mathematics in the common goal of providing a consistently easy and logical understanding of the concepts. (Meaning, let's make Math easy and fun for students.)

Keeping the students as the priority, certain "weird math" gets discarded. For example, did you know that a full pi radian angle is only 180°. If I were to use only pi to cut you a slice of pie that means you would only get half of what you asked for because a circle is really 2π. Using τ you would have access to the full 360°.

All-in-all, I want the focus in learning to be on the learner not the establishment. I encourage you to challenge yourself, question your logic, and most of all keep your eyes open and focused on new horizons.

Happy Tau Day! Now, go enjoy TWO pies!

Pi is a lie. Happy Half Tau Day

Pi is a lie. The concept of Pi (π) is confusing and makes trigonometry more complex than it needs to be. Math can be made easy to learn and understand. Michael Hartl proposes that we reclaim that simplicity through the use of Tau (τ).

Enjoy this video made by a Math student who understands the logic of Tau and the need to increase its popular use.

URL: http://www.youtube.com/watch?v=jG7vhMMXagQ

Intrigued? Try tasting this bit of Tau (excerpt from "The Tau Manifesto"):

The Tau Manifesto is dedicated to the proposition that the proper response to “π is wrong” is “No, really.” And the true circle constant deserves a proper name. As you may have guessed by now, The Tau Manifesto proposes that this name should be the Greek letter τ (tau):

τ ≡ C/r = 6.283185307179586…

Throughout the rest of this manifesto, we will see that the number τ is the correct choice, and we will show through usage (Section 2 and Section 3) and by direct argumentation (Section 4) that the letter τ is a natural choice as well.

Happy Half Tau Day! The complete celebration will come on the 28th of June.