In this video I show how we can treat vectors algebraically by introducing a coordinate system and the concept of a position vector. Since vectors are considered equivalent if they have the same magnitude and direction, then they can be placed anywhere in a coordinate system and still be equivalent. However, if we move that vector such that its tail starts from the origin, then we can consider the coordinates of it's arrow head as the "components" of that vector; which we can represent using triangle brackets and call the "position vector". We can calculate the position vector from any vector that is offset away from the origin by subtracting each of the x, y, and z components from each other from the tail to arrow head coordinates. I also illustrate this concept with an example at the end of the video.
The timestamps of key parts of the video are listed below:
- Components: 0:00 - Equivalent Vectors: 3:00 - Position Vector: 7:09 - Equation 1: 13:10 - Example 3: 13:44
This video was taken from my earlier video listed below:
In this video I start a new series on Giza Pyramid Geometry and show that the mathematical constants pi, e, and the Golden Ratio are all encoded inside the Great Pyramid of Giza. The Great Pyramid of Giza was supposedly built in the early 26th century BC over a period of 27 years as a tomb for the pharaoh Khufu. The original height was 146.6 m and the base has a side length of 230.33 m, with a slope of 51.84 degrees, and a top angle of 76.31 degrees. If we scaled this down such that the height is 4 meters, we obtain several famous mathematical constants. The base side length becomes equal to 2pi and the cross-section slope length becomes pi∙phi where phi is the Golden Ratio. Furthermore, the number e is obtained from the equation 4∙slope / (top angle). Later in the video I do some further trigonometric calculations check for tangent, cosine, and sine of the slope. All the calculations were within 99.93% or more similar to the mathematical constants. This begs the question as to whether this was intentional, a coincidence, or merely the nature of optimal building construction methods and geometry. These questions and more will be explored in further videos!
Also alluded to in the video is that the coordinates of the Giza Pyramid encode the speed of light in m/s, which is also a topic for a future video so stay tuned...
Video links:
- MES Links: https://mes.fm/links
- YouTube playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HIzqSVzEURzhMphO9ePJ22
- Great Pyramid of Giza Wiki: https://en.wikipedia.org/wiki/Great_Pyramid_of_Giza
- Mathematical Encoding in the Great Pyramid: https://www.ancient-origins.net/ancient-places-africa-opinion-guest-authors/mathematical-encoding-great-pyramid-002323
- MES Excel file: https://1drv.ms/x/s!As32ynv0LoaIitEu2xs-6uVQJLBBQg
- Pi (π): https://en.wikipedia.org/wiki/Pi
- e: https://en.wikipedia.org/wiki/E_(mathematical_constant)
- Golden ratio (φ): https://en.wikipedia.org/wiki/Golden_ratio
- ChatGPT to convert angle to degrees: https://chat.openai.com/share/3aafc363-6d43-4f7d-9611-7416d305b0d5
- Pythagorean Theorem: https://en.wikipedia.org/wiki/Pythagorean_theorem .
Timestamps:
- Intro and links: 0:00
- MES Links: 1:15
- Great Pyramid of Giza Wiki: 1:36
- Giza pyramid dimensions: 2:26
- Ancient Origins article: 3:19
- MES Excel file, pi, e, phi, ChatGPT degrees: 4:07
- MES Excel calculations: 5:20
- Original Giza Pyramid dimensions: 6:13
- Pythagorean Theorem: 7:55
- Giza Pyramid scaled to a height of 4 meters: 8:10
- Comparisons with Famous Constants: pi, e, phi: 9:20
- Trigonometry Check: 13:04
- Outro: 15:10
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In this video I go over how to Loop YouTube videos with www.InfiniteLooper.com. It's a simple website that you can search directly YouTube videos and then loop them at specific parts of the video for an infinite time. This is useful whenever you have the random need for looping YouTube videos. Try it out!
Related Videos:
Amazing Google Maps 3D Animation + Gran Fondo Visual Route: http://youtu.be/7otGmGIYO4U
Snapchat Tricks: http://youtu.be/U__a4K22ATM
Replace Samsung S Voice with Google Voice Search on Your Galaxy S4: http://youtu.be/Gcv88jlyQOs
Samsung Trolls Apple - Is it possible to ship $1.05 Billion in 5 cent coins to Apple??: http://youtu.be/X26-0JfAWjo
Using Google Search as a Calculator: http://youtu.be/RxCqjklGw9A
Graphing with the Google Search Part 1: http://youtu.be/1k3QDg2sB4o
Completely Remove Babylon Toolbar/Search/Settings from Google Chrome!!: http://youtu.be/3JenkmYXBWc .
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https://www.youtube.com/watch?v=Rnyxs1ntJMw
In this video I go over the trig product identities and provide a simple proof for them. The identities I cover are listed below:
sin(x)cos(y) = 1/2 [sin(x+y) + sin(x-y)]
cos(x)cos(y) = 1/2[cos(x+y) + cos(x-y)]
sin(x)sin(y) = 1/2[cos(x-y) - cos(x+y)]
In proving the above identities I make use of the identities which I covered in my earlier video (see the related videos below), specifically the identities for sin(x+/-y) and cos(x+/-y).
Download the notes in my video: http://1drv.ms/1DZu6XH
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometry-product-identities
Related Videos:
Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs
Trigonometry Identities: sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y): http://youtu.be/edtk9thfwbM
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Half Angle Trigonometry Identities: http://youtu.be/0bY6tHZhBSI .
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https://www.youtube.com/watch?v=os8XKWAj9P8
In this video my brother, MFA, goes over a tutorial on the biggest mobile app out there and first app to use Augmented Reality Technology, Pokemon Go. If you have played Pokemon Go you might have realized that it is difficult and time consuming to increase your Pokemon trainer's level. But there is a way to increase your XP fast and it involves collecting many Pidgeys and Weedles and then activating your lucky egg. This is part of the step and the rest of the steps are in the video so make sure to watch it as it will help you.... catch em all!
Try out our latest Pokemon Go Calculator: http://pgc.mes.fm
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhskrdm31EjQQvAuMIw
Related Videos:
Deodorant vs. Antiperspirant: https://youtu.be/ofSXC2WydcE
View Subscriber Count Without Unsubscribing: http://youtu.be/vxYw3ZRUdKo
Difference Between Expresso and Coffee: http://youtu.be/0zcRNLfOMIg
Poker: What is Equity?: http://youtu.be/xhZOfQGteAo
Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
What is 20/20 Vision?: http://youtu.be/31kYnnIjugQ
NCAA vs. NBA 3 Point Line: http://youtu.be/1__25TpOdB0
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
NBA Free Agency and Max Contracts: Introduction: http://youtu.be/osDN-bnPULY .
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https://www.youtube.com/watch?v=RMXghsq88Ag
In this video I derive how to do the derivative for a function that has another function in it, for example y = sin(x^5+x^3). This rule is the chain rule and is one of the most important and useful derivative rules in all of calculus and mathematics.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIidgzupbHXCdgeJAxRg?e=EmTrtX
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-rules-proof-of-chain-rule
Related Videos:
Derivative of y = a^x and e^x: Using the Chain Rule: http://youtu.be/uXwwgMzikao
Derivative Examples using the Chain Rule: http://youtu.be/KB9_lBxTrwI
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
Derivative of Trigonometry Functions: Derivative of sin(x): http://youtu.be/elEvQ4Wu7Pk .
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In #911Truth Part 23, I have uploaded a slowed down version of the WTC 1 North Tower's "Spire" core columns, which somehow remained standing after WTC 1 turned to dust, only to shortly afterwards literally turn to dust before our very eyes. There is also another key part of the Spire that many people, including me, had missed all these years. There are a group of core columns that turn to dust just before the Spire does, and even more clearly too! Truly mind-boggling! This was brought to my attention by my subscriber HeyOdi during my recent 9/11 Emergency Broadcast livestream, but even then I didn't understand what they meant until moments after the livestream ended.
After these other core columns turned to dust, the Spire stood upright for a few more seconds, before it too turned to dust as it gradually falls downwards. Note that the Spire is 900 feet tall, which is almost the height of the Eiffel Tower! So, unless there is a 900 ft hole in the ground, it's safe to conclude the tower turned to dust, and it certainly wasn't seen in the rubble afterwards. Also note that Stairwell B was near the bottom of the Spire, but nothing landed on top of Stairwell B or the 16 survivors on or near Stairwell B. Truly mind boggling stuff!
This video was taken from the 2:52 mark of the following video:
- WTC 9/11 Video by WNBC-TV Unknown w/ Reporter Joe Avellar (Enhanced Video/Audio & Doubled FPS): https://youtu.be/3MWuaEMfPLM
The timestamps of key parts of the video are listed below:
- WTC 1 North Tower turning to dust: 0:00
- Spire standing upright, other core columns LITERALLY turning into dust: 0:10
- Spire turns into dust as it falls downwards: 0:28
- Keep your eyes on the other core columns: 0:37
- 0.1X speed: Other core columns turning to dust: 0:49
- Height comparison: Spire, WTC 1, Eiffel Tower, Building 7: 1:28
- 0.1X speed: Spire falling into dust (or a 900 foot hole??): 1:47
Stay tuned for #911Truth Part 24...
- HIVE video screenshots: https://peakd.com/hive-113182/@mes/911truth-part-23-spire-turning-to-dust
Related Videos:
#911Truth video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EzqTamtIXtgX8QudQSxuxh and https://peakd.com/truth/@mes/911
9/11 Observable Evidence video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_HHWt33moIqEeUBP3cgCh .
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https://www.youtube.com/watch?v=wJazsgxeuFc
In my earlier video I went over the rules and did some examples on 10 pin bowling scores. In this video I show a 10 Pin Bowling Calculator that I created using Microsoft Excel 2007. The calculator is very useful and you can download it for free below!
Download the notes in my video:
10 Pin Bowling Calculator: https://www.dropbox.com/s/wzygfevs08ufb5w/257%20-%2010%20Pin%20Bowling%20Calculator.xlsx
PDF Notes: https://www.dropbox.com/s/5uvga0u70lt8vse/257%20-%2010%20Pin%20Bowling%20Calculator.pdf
Related Videos:
Bowling Scoring System: 10 Pin Bowling: http://youtu.be/EsMocP3Gx-g
5 Pin Bowling - Scoring and Free Calculator to Download: http://youtu.be/ezXX5RlHRXk .
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https://www.youtube.com/watch?v=hhDXMTwvTu8
In this video I rewrite my earlier formula on rotating a vector and this time rewrite it in matrix form. This results in deriving the Rotation Matrix, which is a very important concept in all of mathematics and physics.
This video was taken from my earlier video listed below:
- Complex Numbers as Rotation Matrices: https://youtu.be/Mgp2vrQeLEw
- Video notes: https://peakd.com/hive-128780/@mes/complex-numbers-as-rotation-matrices
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0E6x0dZEAx77Kqv7LLxYdbx
Related Videos:
Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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In this video I go further into exploring examples on limits where you can not simply solve them right away but require to break them up into separate functions and apply the one-sided-limit approach in solving them. Basically for functions that are 2 in one such as absolute value type functions, you need to first find the limit by approaching the x-value from the left and from the right sides of it and the limit exists if and only if you approach the same limit from both sides. These are very useful examples so make sure to watch!
Download the notes in my video: https://www.dropbox.com/s/9czzjdftiq7qd6l/274%20-%20Limits%20-%20Examples%20Part%202.pdf
Related Videos:
One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
Limits - Examples Part 1: http://youtu.be/lczWvRBw60A
Absolute Values - Properties and Rules: http://youtu.be/tl9iten87MU
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws Part 2 - Examples + Intro to Direct Substitution Property: http://youtu.be/cIjWhV7YdOE
Limits - where Direct Substitution doesn't work: http://youtu.be/L9jrwf-IKeU
The Limit of a Function: http://youtu.be/0RX1o7KeZ28 .
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https://www.youtube.com/watch?v=9O6UFASe4F8