## Profile

Marvin Dave Ganza

Worked at City Assessor's Office - La Carlota City

Attends Lasaltech Inc. La Carlota

Lived in La Carlota City, Philippines

268 followers|58,109 views

AboutPostsPhotosYouTube

## Stream

### Marvin Dave Ganza

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

### Marvin Dave Ganza

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

### Marvin Dave Ganza

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

### Marvin Dave Ganza

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

### Marvin Dave Ganza

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

### Marvin Dave Ganza

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

### Marvin Dave Ganza

Shared publicly -Please vote my entry! Just go to this link:

https://www.purpleleaves.de/en/submission/football-revolution-by-marvin-dave--14396.html

then log-in using your fb account then click the "awesome"! Thank you!

https://www.purpleleaves.de/en/submission/football-revolution-by-marvin-dave--14396.html

then log-in using your fb account then click the "awesome"! Thank you!

1

### Marvin Dave Ganza

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

### Marvin Dave Ganza

Shared publicly -This is what happens when you take ‘simplify and add lightness’ to the extreme – a new motorbike from #Lotus

http://www.TOPGEAR.com/uk/car-news/lotus-has-built-an-amazing-motorbike-2013-02-20

http://www.TOPGEAR.com/uk/car-news/lotus-has-built-an-amazing-motorbike-2013-02-20

1

People

In his circles

336 people

Work

Employment

- City Assessor's Office - La Carlota City2012 - 2012

Places

Previously

La Carlota City, Philippines

Links

YouTube

Other profiles

Story

Tagline

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

Education

- Lasaltech Inc. La CarlotaComputer Programming NCIV, 2012 - present
- University of Saint Louis TuguegaraoBachelor of Science in Electrical Engineering, 2004 - present

Basic Information

Gender

Male