Start a hangout

## Profile

Razz Navareth

Works at PHP, HTML, JAVA, MySQL, C, C++

Attended University of Saint Louis Tuguegarao

Lived in La Carlota City, Philippines

299 followers|87,650 views

AboutPostsPhotosYouTube

## Stream

### Razz Navareth

Shared publicly -Hey, #TheWalkingDead fans out there who patienly waiting for feb. 8, 2014 like me. Enjoy your #Christmas break! #TWD

1

### Razz Navareth

Shared publicly -**Reverse Arrow Optical Illusion**

**Look Mah; I can do magic!**This is a nice experiment to do with the kids.

This is simply a demo of refraction: bending of light. #scienceeveryday

A whimsical example:

https://plus.google.com/u/0/113881433443048137993/posts/MgCxqhMsngq

Sources:

Gif extracted from: http://youtu.be/G303o8pJzls

Physics Central info on Refraction: http://thekidshouldseethis.com/post/79356632627

1

### Razz Navareth

Shared publicly -Expedition 38 crew members pose for an in-flight crew portrait in the Kibo laboratory of the International Space Station on Feb. 22, 2014. Pictured (clockwise from top center) are Russian cosmonaut Oleg Kotov, commander; Japan Aerospace Exploration Agency astronaut Koichi Wakata, Russian cosmonaut Sergey Ryazanskiy, NASA astronauts Rick Mastracchio and Mike Hopkins, and Russian cosmonaut Mikhail Tyurin, all flight engineers.

Image Credit: NASA

#iss #space #exp38 #nasa #spacestation #portrait, #roscosmos #jaxa

Image Credit: NASA

#iss #space #exp38 #nasa #spacestation #portrait, #roscosmos #jaxa

1

### Razz Navareth

Shared publicly -“You can look at a picture for a week and never think of it again. You can also look at a picture for a second and think of it all your life.”

― Joan Miró

'Petunia's Portrait'

#hqspanimals +HQSP Animals curated by +Alejandro J. Soto +Krystina Isabella Brion +Andy Smith +Squirrel Saturday #squirrelsaturday +Skippy Sheeskin +Beth Blackwell #squirrelphotography

― Joan Miró

'Petunia's Portrait'

#hqspanimals +HQSP Animals curated by +Alejandro J. Soto +Krystina Isabella Brion +Andy Smith +Squirrel Saturday #squirrelsaturday +Skippy Sheeskin +Beth Blackwell #squirrelphotography

1

In his circles

336 people

### Razz Navareth

Shared publicly -WHERE #CHRISTMAS CAME FROM?

"Long before the birth of # Christ, the Jews celebrated an eight-day Festival of Lights, and it is believed that the Germanic peoples held a great festival not only at midsummer but also at the winter solstice, when they celebrated the birth of the sun and honored the great fertility gods Wotan and Freyja, Donar(Thor) and Freyr. Even after the Emperor Constantine (A.D. 306-337) declared Christianity to be Rome's official imperial religion, the evocation of light and fertility as an important component of pre-Christian midwinter celebrations could not be entirely suppressed. In year 274 the Roman Emperor Aurelian (A.D. 214-275) had established an official cult of the sun-god Mithras, declaring his birthday, December 25, a national holiday. The cult of #Mithras, the Aryan god of light, had spread from Persia through Asia Minor to Greece, Rome, and as far as the Germanic lands and Britain. Numerous ruins of his shrines still testify to the high regard in which this god was held, especially by the Roman legions, as a bringer of fertility, peace, and victory. So it was a clever move when in year A. D. 354, the Christian church under #Pope #Liberius(352-366) co-opted the birthday of Mithras and declared December 25 to be the birthday of Jesus Christ."

SOURCE: The 48 Laws of Power by Robert Greene

Image: Mahanaim Resort, Iloilo, #Philippines(Taken by me via nokia 302 only)

"Long before the birth of # Christ, the Jews celebrated an eight-day Festival of Lights, and it is believed that the Germanic peoples held a great festival not only at midsummer but also at the winter solstice, when they celebrated the birth of the sun and honored the great fertility gods Wotan and Freyja, Donar(Thor) and Freyr. Even after the Emperor Constantine (A.D. 306-337) declared Christianity to be Rome's official imperial religion, the evocation of light and fertility as an important component of pre-Christian midwinter celebrations could not be entirely suppressed. In year 274 the Roman Emperor Aurelian (A.D. 214-275) had established an official cult of the sun-god Mithras, declaring his birthday, December 25, a national holiday. The cult of #Mithras, the Aryan god of light, had spread from Persia through Asia Minor to Greece, Rome, and as far as the Germanic lands and Britain. Numerous ruins of his shrines still testify to the high regard in which this god was held, especially by the Roman legions, as a bringer of fertility, peace, and victory. So it was a clever move when in year A. D. 354, the Christian church under #Pope #Liberius(352-366) co-opted the birthday of Mithras and declared December 25 to be the birthday of Jesus Christ."

SOURCE: The 48 Laws of Power by Robert Greene

Image: Mahanaim Resort, Iloilo, #Philippines(Taken by me via nokia 302 only)

1

### Razz Navareth

Shared publicly -*"Vince Reffet and Fred Fugen, members of the French BASE jumping team Soul Flyers, set a new world record after taking a dive off the top of the world's tallest building: Dubai's Burj Khalifa."*

Wowza! My heart rate went up while watching this video. Can't even imagine what it'd be like to actually make a jump like that.

More:

http://www.thedailybeast.com/articles/2014/04/23/viral-video-burj-khalifa-base-jump.html

1

### Razz Navareth

Shared publicly -#friday #weekend #TGIF #foodfriday #food #happyfriday

I'm ready for weekend! +David Seeyaah

###Circle and Share me for Awesome pictures, videos, and more###

#caturdayeveryday #cats #caturdayeveryday #funny

I'm ready for weekend! +David Seeyaah

###Circle and Share me for Awesome pictures, videos, and more###

#caturdayeveryday #cats #caturdayeveryday #funny

1

### Razz Navareth

Shared publicly -**Tidal Forces**

This illustrates how the Moon causes tides on the Earth.

The Moon’s gravity pulls on each piece of the Earth, but the attractive force is a little stronger on the side facing the Moon, and a little weaker on the side opposite the Moon. The average force is the force at the center of the Earth.

The arrows at each point show how much the attractive force differs from the average as the Moon circles the Earth. These are the

*tidal forces*, and the result is a bulge in the ocean on opposite sides of the Earth. Earth rotates under these bulges, resulting in about two high tides each 24 hours.

Source: WolframAlpha demonstrations.

#gravity #astrophysics

1

### Razz Navareth

Shared publicly -The definition extracted from Wikipedia:

Construction:

If the Wikipedia one was a bit hard to understand here's how I think of it:

Starting with a 3,4,5 right triangle, if you think of the sides of the triangle as each being one of the sides of a square, the areas of the two smaller squares add up to the area of the larger square.

Now thinking of the two smaller sides (in this case, 3 and 4) as being the bases of two other 3, 4, 5 right triangles. As long as the ratios are equivalent, a right triangle with sides 9/5,12/5,3 has the exact same angle and side ratios as a right triangle of sides 3,4,5, a right triangle with sides 12/5,16/5,4

Each triangle is geometrically similar to the first as the angle-angle and side-side ratios are the same for each

The beauty of the fractal is that if you look at simply a single triangle and the three squares involved with said triangle, the "tree" (trunk as largest square and branches as two smaller squares) is basically the same as any other triangle-and-three-square figure in the whole fractal.

The area can be determined as follows

S₁² + S₁² = L²

2S₁² = L²

S₁² = L²/2

S₁ = L/√2

Similarly:

S₂ = S₁/√2 = (L/√2)/√2 = L/(√2)²

S₃ = S₂/√2 = (L/(√2)²)/√2 = L/(√2)³

S₄ = S₃/√2 = (L/(√2)³)/√2 = L/(√2)⁴

. . .

Sn = L/(√2)ⁿ

We start with 1 square

In each iteration, we add twice the number of square added in previous iteration

In iteration 1, we add 2 squares

In iteration 2, we add 2*2 = 2² squares

In iteration 3, we add 2*2² = 2³ squares

In iteration 3, we add 2*2³ = 2⁴ squares

. . .

In iteration n, we add 2ⁿ squares

So in each iteration, we add 2ⁿ squares, each with side length of L/(√2)ⁿ

Area of all squares in iteration n

= number of squares * area of each square

= number of squares * (side length )²

= 2ⁿ * (L/(√2)ⁿ)²

= 2ⁿ * L²/2ⁿ

= L²

= Area of original square

So why does Wikipedia get total area = 1?

Because, they have obviously assumed that dimension of original square = 1 x 1, which means L = 1, therefore L² = 1. However, this is NOT explicitly stated in the link, which it should have been, since the last mention of original (i.e. largest) square assumes square of size L x L, not 1 x 1.

http://www.redbubble.com/groups/apophysis-tutorial-fun/forums/14903/topics/332497-volume-64-pythagoras-trees

http://www.wolframalpha.com/input/?i=pythagoras+tree

http://math.mercyhurst.edu/~credmond/computer_art/artwork/pythagoras.php

*The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942,[1] it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem. If the largest square has a size of L × L, the entire Pythagoras tree fits snugly inside a box of size 6L × 4L.[2][3] The finer details of the tree resemble the Lévy C curve.*Construction:

*The construction of the Pythagoras tree begins with a square. Upon this square are constructed two squares, each scaled down by a linear factor of ½√2, such that the corners of the squares coincide pairwise. The same procedure is then applied recursively to the two smaller squares, ad infinitum. The illustration below shows the first few iterations in the construction process*If the Wikipedia one was a bit hard to understand here's how I think of it:

Starting with a 3,4,5 right triangle, if you think of the sides of the triangle as each being one of the sides of a square, the areas of the two smaller squares add up to the area of the larger square.

Now thinking of the two smaller sides (in this case, 3 and 4) as being the bases of two other 3, 4, 5 right triangles. As long as the ratios are equivalent, a right triangle with sides 9/5,12/5,3 has the exact same angle and side ratios as a right triangle of sides 3,4,5, a right triangle with sides 12/5,16/5,4

**The Pythagoras tree emerges by continuing this process many, many times (as needed).**Each triangle is geometrically similar to the first as the angle-angle and side-side ratios are the same for each

The beauty of the fractal is that if you look at simply a single triangle and the three squares involved with said triangle, the "tree" (trunk as largest square and branches as two smaller squares) is basically the same as any other triangle-and-three-square figure in the whole fractal.

**Thinking of Pythagorean Theorem in a physical sense was easy to understand by me**The area can be determined as follows

*By Pythagorean theorem*:S₁² + S₁² = L²

2S₁² = L²

S₁² = L²/2

S₁ = L/√2

Similarly:

S₂ = S₁/√2 = (L/√2)/√2 = L/(√2)²

S₃ = S₂/√2 = (L/(√2)²)/√2 = L/(√2)³

S₄ = S₃/√2 = (L/(√2)³)/√2 = L/(√2)⁴

. . .

Sn = L/(√2)ⁿ

We start with 1 square

In each iteration, we add twice the number of square added in previous iteration

In iteration 1, we add 2 squares

In iteration 2, we add 2*2 = 2² squares

In iteration 3, we add 2*2² = 2³ squares

In iteration 3, we add 2*2³ = 2⁴ squares

. . .

In iteration n, we add 2ⁿ squares

So in each iteration, we add 2ⁿ squares, each with side length of L/(√2)ⁿ

Area of all squares in iteration n

= number of squares * area of each square

= number of squares * (side length )²

= 2ⁿ * (L/(√2)ⁿ)²

= 2ⁿ * L²/2ⁿ

= L²

= Area of original square

So why does Wikipedia get total area = 1?

Because, they have obviously assumed that dimension of original square = 1 x 1, which means L = 1, therefore L² = 1. However, this is NOT explicitly stated in the link, which it should have been, since the last mention of original (i.e. largest) square assumes square of size L x L, not 1 x 1.

**More designs using Pythagoras tree**:http://www.redbubble.com/groups/apophysis-tutorial-fun/forums/14903/topics/332497-volume-64-pythagoras-trees

**Draw on your own**:http://www.wolframalpha.com/input/?i=pythagoras+tree

http://math.mercyhurst.edu/~credmond/computer_art/artwork/pythagoras.php

1

People

In his circles

336 people

Collections Razz is following

Education

- University of Saint Louis TuguegaraoBachelor of Science in Electrical Engineering, 2008 - 2012
- Lasaltech Inc. La CarlotaComputer Programming NCIV, 2012 - 2014

Basic Information

Gender

Male

Apps with Google+ Sign-in

- Clash of Clans
- Fast & Furious:Legacy
- Plants vs. Zombies 2

Story

Tagline

Ow! You opened my page! So, what's your next plan?

Work

Employment

- PHP, HTML, JAVA, MySQL, C, C++Home-Based Programmer, present

Places

Previously

La Carlota City, Philippines

Links

YouTube

Other profiles