Putting 3D in Perspective: Projecting a 3D Rectangle to 2D
In this video I project a 3D rectangle onto a 2D screen, while also removing a segment of a line that is behind the rectangle so that it maintains its 3D perspective. I first project the given 3D rectangle coordinates using the 3D to 2D projection equation I derived earlier. Then, I determine the point of intersection of the 3D rectangle and 3D line. The next point that is needed is the point of intersection of the projected 2D line and the bottom portion of the projected 2D rectangle. Once I solve for these, I use GeoGebra to plot the projected line while removing the portion that is behind the rectangle. The resulting 3D chart is truly amazing! https://www.geogebra.org/calculator/twezjbu5
The timestamps of key parts of the video are listed below:
- Question 4: Projecting a 3D rectangle to 2D: 0:00 - Solution: Graphing out the rectangle and its projection in GeoGebra: 1:04 - Remove the portion of the line behind the rectangle: 6:12 - Find point of intersection of the 3D line and rectangle: 7:15 - Determining the equation of the plane of the rectangle: 7:47 - Cross product to get the plane normal vector: 15:48 - Calculating the equation of the plane: 21:12 - Plugging in the line equation into the rectangle equation: 27:03 - Graphing the intersection point in GeoGebra: 32:18 - Finding the point of intersection of the projected line and rectangle: 35:03 - Vector equation of bottom right portion of projected rectangle: 38:08 - Equating the projected line equation with the bottom right rectangle line equation: 41:07 - Calculating the point of intersection of projected line and rectangle: 47:10 - Graphing it all out in GeoGebra: 50:30
In #911Truth Part 18 I have uploaded, with permission, legendary documentary maker Christian Hampton's, from Wolf Clan Media, first 9/11 documentary titled: 9/11 Alchemy: Free Energy & Free Thinking. This documentary is Volume 1 of his 9/11 Alchemy series in which I have already uploaded Volume 2, Facing Reality, in #911Truth Part 11. But given the importance of both free energy and free thinking, now is a fitting time to present it. In fact, the simple notion of “thinking freely” is something that is deemed “controversial” in today’s totalitarian fear-based order-following society.
The documentary begins with an overview of Nikola Tesla and his plans to build Wardenclyffe Tower in New York in 1901 with hopes of providing the world with unmetered free electrical energy. Fast forward through decades of pre-planned wars, narrated via President Dwight D. Eisenhower’s warning of the Military Industrial Complex, and we arrive at the new ground zero for war: September 11, 2001. The turning of massive buildings (and people) into dust and spontaneously combusting cars, all while leaving very little rubble left was a devastation that left clues for a better world, a free world.
September 11, 2001 was the date the world was confronted with the magic of alchemy, but we just need the mind to comprehend what the eyes see. Dr. Judy Wood was one such mind and even connected the work of obscure free thinking inventor John Hutchison to every alchemical effect on 9/11. What we are entering is the world of secrecy, the world of classified material, the world which the public is not meant to see or even know about. And this world has ways of keeping itself hidden. One such way is by steering truth seekers away from cold fusion and into dead ends of invisible thermitic explosives. But steer through the clouds of dust and disinformation, and what’s laying there is the truth. And this truth is that free energy and free thinking go hand-in-hand…
Subscribe to @Wolf Clan Media! https://www.youtube.com/user/SyllablezShow/videos
WCM website: http://wolfclanmedia.org/
For a complete list of WCM links, complete sequence of events, and MANY screenshots chronicling the video, please see the corresponding video notes on the Hive blockchain: https://peakd.com/hive-113182/@mes/911truth-part-18-9-11-alchemy-free-energy-and-free-thinking-by-wcm
The (shortened) sequences of events and their timestamps are listed below.
1. @ 0:00 - Nikola Tesla
2. @ 5:49 – September 11, 2001
- @ 6:54 – Hurricane Erin mentioned on TV
3. @ 13:28 – 9/11 Alchemy: Free Energy & Free Thinking
4. Disappearing Towers
- @ 19:00 – Miracle of Stairwell B
5. @ 21:35 – John Hutchison: The Hutchison Effect
- @ 24:56 - Dustification of Humans
6. @ 32:55 – Dustification of the WTC
7. @ 36:31 – Dust
8. @ 42:07 – More Hutchison Effect on 9/11
9. @ 51:42 – Molecular dissociation
10. @ 53:52 – Energy
11. @ 1:09:15 – Joseph Newman free energy device
12. @ 1:10:36 – NIST WTC 7 science fraud
13. @ 1:11:50 – ARA and SAIC chosen to coverup Twin Towers dustification
14. Cold Fusion and 9/11
- @ 1:14:49 – High tritium levels on 9/11
- @ 1:16:03 – Disinfo agent Steven E. Jones coverup of LENR or Cold Fusion
15. @ 1:24:38 – Disinfo agent Steven E. Jones and “Nano-Thermite” disinfo
16. @ 1:28:00 – Alleged “planes”, bird damage, and aluminum can launcher
17. @ 1:29:54 – Cleanup crew footage from 9/11 to 9/13
18. @ 1:30:08 – Bill Cooper predicts 9/11
Stay tuned for #911Truth Part 19...
Related Videos:
✈️#911Truth Part 11: Feature Documentary: 9/11 Alchemy – Facing Reality by Wolf Clan Media: https://peakd.com/terrorism/@mes/911truth-part-11-feature-documentary-9-11-alchemy-facing-reality-by-wolf-clan-media
#911Truth video series: https://peakd.com/truth/@mes/911
#MESScience video series: https://mes.fm/science-playlist
#MESExperiments video series: https://peakd.com/mesexperiments/@mes/list
#AntiGravity video series: https://peakd.com/antigravity/@mes/series
#FreeEnergy video series: https://mes.fm/freeenergy-playlist .
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In this video I go over further into Conic Sections in Polar Coordinates and this time expand in detail on the variations in the polar equations theorem that stems from the unified theorem for conics which I covered in my last video. Recall that the Unified theorem involves defining parabolas, ellipses, and hyperbolas by a single theorem involving just a focus and a directrix; this I will prove is in fact true in later videos so stay tuned! As explained in my earlier video, this theorem has the benefit of also being able to write a simple formula for conics in polar coordinates. In this particular video, I expand on the various variations of the resulting polar equations. The polar equations depend on where the directrix is located and I explain 4 different cases: x = +/- d and y = +/- d. The horizontal conics involve the cosine function, while the vertical conics involve the sine trigonometric function. This is a very important video in understanding the different variations of polar equations for conics and in understanding the need for this unified conics theorem, especially as I move further into the proof of the theorem; so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5lRmZoe0Rmx2yOxUQ
View video notes on the Hive blockchain: https://peakd.com/steemstem/@mes/shifted-conics-in-polar-coordinates-variations-in-polar-equations-theorem
Related Videos:
Conics in Polar Coordinates: Unified Theorem for Conic Sections: https://youtu.be/eUvzyxCfJCw
Conic Sections: Hyperbola: Definition and Formula: https://youtu.be/UBIHovXNV9U
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: Infinite Representations: https://youtu.be/QJYbnO7NzCk
Polar Coordinates: https://youtu.be/-KAdZL-N4ok .
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In this video I go further into Polynomial Long Division by going over some very useful examples. I also show how factoring is possible if the remainder is zero, which is a great property to keep in mind whenever you are dividing polynomials.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIibEQK2MJPoReCq9eeQ?e=bzrZnV
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/polynomial-long-division-examples
Related Videos:
Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y
Long Division by Hand - An in depth look: http://youtu.be/giBZg5Vqryo
Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE .
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In this video I go over another example on Polar Coordinates, and this time look at revisiting the Cardioid, or Heart, example in my earlier video and determine the formula for the slope or tangent to the curve. This video goes over just determining the formula, in which I will solve the slopes in various cases and angles in later video so stay tuned for that. Determining the formula of the slope of a tangent line to the curve involves following the same method as in my last video on Tangents to Polar curves. Namely, first writing the polar curve equation into Parametric Equations and then apply the formula for the derivative using Parametric Calculus. Doing this we can a formula that involves many trigonometric terms, which I decided to simplify (because my Calculus book does so), and thus go over some pretty interesting factoring and trig algebra. This is a very interesting video into determining the slope of a polar curve, but even more so is the trigonometric algebra, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvM_LvGHjQ4M00FUhw
View video notes on the Hive blockchain: https://peakd.com/@mes/g8fcn-video-notes-polar-coordinates-example-9-cardioid-part-1-slope-formula-and-trigonometric-algebra
Related Videos:
Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY
Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM
Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE
Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY
Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE
Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A
Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs
Polar Coordinates: Example 3: Cartesian to Polar: https://youtu.be/mV-9KTQM-RU
Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw .
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In this video I go over scalar multiplication for vectors. The idea behind scalar multiplication is wanting to multiply a vector by a real number c such that it becomes shorter or longer but in the same parallel direction. In other words, the real number c "scales" the vector. And when multiplying by a negative number, the vector flips in the opposite direction. When dealing with negative vectors, we can visualize this by subtracting vectors using the Parallelogram or Triangle Laws. I also go over an example to illustrate scaling and adding vectors.
The timestamps of key parts of the video are listed below:
- Definition of Scalar Multiplication: 0:00
- Negative Vectors: 3:00
- Example 2: 6:11
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: Vectors: https://youtu.be/0lJiVlKw4Kc
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EiRECLVkBCcFhSpbSz8XIw
Related videos:
Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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In this video I go over an example on differential equations and show that the family of functions y = (1 + ce^t) / (1 - ce^t), where c is a constant, is a solution to the differential equation y' = 1/2(y^2 - 1). The process of proving that it is indeed a solution is to simply take the derivative of the family of functions and ensure that it satisfies the differential equation, which I show that it clearly does.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsFwy6vbLODQ0spUnA
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-example-1
Related Videos:
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Derivative Rules - Proof of the Quotient Rule: http://youtu.be/fJcgnLKkISE
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ .
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https://www.youtube.com/watch?v=n575RKO48Ro
In #911Truth Part 7 I go over the strategy employed by Controlled Opposition Groups and their main goal: stray people away from looking at the facts as much as possible because the Truth cuts right through to your subconscious.
To understand how and why controlled opposition groups work, it is first important to see just how powerful and ignored our Subconscious, or known as “Gut”, Intuition, or even just “BS Detector”, really is. When people are presented with information, often times they will have a distinct “feeling” towards that information, either positive or negative even if they are not consciously aware of it; much like driving a car in which you daze off but still get to your destination in one piece. Controlled Opposition groups work by mixing in real and false information so that the people that can see through the blatant mainstream lies are still less likely to jump on board the alternative mixture of lies, because the subconscious still knows something is not right. Thus other factors play a larger role such as “Authority”, Social Stigma, and if having an opinion on the topic is even worth it. But when someone is presented with the absolute unmuddied truth, the subconscious can feel right away to wake up your conscious brain and investigate further! This was exactly my experience when I heard about the simple question “Where Did The Towers Go?” in which my entire life flashed before my eyes and I felt the need to explore further into 9/11; something which wasn’t the case when I heard simple chants of “9/11 was an inside job”. And when #FreeEnergy was tied directly with 9/11, I knew from that moment on that there was no going back and my lifelong goal of developing #FreeEnergy has just begun!
My experience is a good example of why Controlled Opposition groups are literally anywhere and everywhere!` Some examples of almost certain controlled psychological operation groups that I cover in this video is Alex Jones, InfoWars, “AlienScientist”, David Icke, “Flat Eart”, and the highly coordinated disinformation campaign regarding the California Forest Fires being used to mix in Directed Energy Weapons as a way to discredit from the irrefutable 9/11 – DEW connection. What makes these groups almost certainly controlled is not necessarily what information they are pushing but rather the information they leave out or purposely spread misinformation about, and just so happens to be about the most important event of our lifetimes: 9/11. Not only that but the site traffic of these websites are MUCH larger than actual truth website such as DrJudyWood.com and RichPlanet.net. But even these controlled groups are absolutely tiny in comparison to the Mainstream Media which literally make the entirety of “alternative” media irrelevant. Thus quite literally there is NO alternative media, but instead there are just a handful of truthful people that desperately need you to wake up and help out!
Also in this video, I cover some corrections and clarifications from Part 6 regarding the “Meteorite”, Lone Filing Cabinet, and the relevant Kingdome height for WTC rubble comparisons.
This was another extensive video on 9/11 which illustrates just how big of an impact it has on nearly all aspects of life and global politics,; and why the controlled opposition groups and PsyOps will continue forever until #FreeEnergy is finally disclosed to the public...
Stay Tuned for #911Truth Part 8…
CORRECTION: @10:24 Kingdome Cylinder Height is just OVER not under 1/5th the WTC 7 Height.
PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIh5Bwv78OnP8YtbyfGA
View video notes on the Hive blockchain: https://peakd.com/terrorism/@mes/911truth-part-7-how-controlled-opposition-works-alex-jones-cali-dew-fires-flat-earth-more
Related Videos:
#911Truth: https://peakd.com/truth/@mes/911
#MESScience: https://mes.fm/science-playlist
#MESExperiments: https://peakd.com/mesexperiments/@mes/list
#AntiGravity: https://peakd.com/antigravity/@mes/series
#FreeEnergy: https://mes.fm/freeenergy-playlist .
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In my earlier videos I went over a useful strategy for integration but with that a very important question arises: can we use our integration strategy to integrate all continuous functions? The answer to that question is unfortunately NO, well at least not in terms of the regular elementary functions. In this video I go over what elementary functions are and explain how most elementary functions, such as e^(x^2) can not be integrated in terms of basic elementary functions. One method to prove whether or not a function can be integrated in terms of elementary functions is called the Risch Algorithm and was developed in 1968 by the American Mathematician Robert Henry Risch.
In my later videos I will go over how functions such as e^(x^2) can be integrated in terms of infinite series so stay tuned for that!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhd4iIg7HrqROZAvF2w
Related Videos:
Strategy for Integration: Examples 2 to 5: http://youtu.be/3JGU3vJsPIk
Strategy for Integration: Example 1: http://youtu.be/xqwRpvdrD6Y
Strategy for Integration: http://youtu.be/7JxW2N7izF0
Integration by Partial Fractions: http://youtu.be/r07NnKf76og
Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo
Integration by Parts: Proof: http://youtu.be/TZhEOct5u_M
The Substitution Rule for Integrals: http://youtu.be/VsLC-0g6hVg
Trigonometric Integrals: Guidelines for sin(x)cos(x): http://youtu.be/aE8Sz5BdMT8
Trigonometric Integrals: Guidelines for tan(x)cos(x): http://youtu.be/oz5nXlYQPB0 .
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https://www.youtube.com/watch?v=OFEDLJYqYps
In this video I go over Part 3 of Example 9 on Polar Coordinates, and this time look at Question B which looks at determining the points at which the tangents lines are either horizontal or vertical. I use the formula for the derivative or slope of a tangent line to the polar cardioid (i.e. heart shaped) curve r = 1 + sinϴ in determining the vertical and horizontal tangents. The horizontal tangents are when the derivative is equal to 0, while the vertical tangents occur when the derivative approaches infinity. When we look at the derivative in terms of its parametric equivalent, in which ϴ is the parameter, we notice that the conditions that need to be met are when dy/dϴ = 0 for horizontal tangents and dx/dϴ = 0 for vertical tangents. But it is very important to realize the special case when both dy/dϴ and dx/dϴ = 0, in which we will get an undefined 0/0 result. But luckily we can use the L’Hospital’s Rule to evaluate these cases to determine if the denominator or numerator is approaching 0 “faster”, which governs whether the result approaches 0 or approaches infinity. In this video, this special case arises and I show that it does in fact approach infinity. This is an extremely detailed and thorough video that takes many different concepts from L’Hospital’s Rule and Trigonometry to Polar and Parametric calculus in order to solve for vertical and horizontal tangent lines, so make sure to watch this whole video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvQCHR0c727P_-7rSg
View Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-9-cardioid-part-3-question-b
Related Videos:
Polar Coordinates: Example 9: Cardioid: Part 2: Question A: https://youtu.be/gUYmzZ8Cfhg
Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra: https://youtu.be/MlIhueP36EE
Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY
Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM
Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE
Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY
Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE
Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A
Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs
Polar Coordinates: Example 3: Cartesian to Polar
Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
L'Hospital's Rule a
...
https://www.youtube.com/watch?v=-TZHaTjHfb8