YouTubeEscapee3

We use vector algebra to solve a nice geometry problem that was discussed recently on the channel "Math Booster". Link to the "Math Booster" video https://www.youtube.com/watch?v=ryNxir6Br9M LinkedIn group "Pre-University Geometric Algebra" https://www.linkedin.com/groups/8278281/

Timestamps are provided below for your convenience. We use GA's rotations and outer products of vectors to find the missing length that will enable us to then solve the problem via the Law of Cosines. Timestamps: 00:00 Introduction 01:00 A pdf of the solution is available online 01:07 Outline of the video 01:41 Ideas that we will use in the solution 03:03 Solution Strategy 03:35 GA formulation of the problem 04:35 Solution 07:45 *** Verification of the solution via an interactive GeoGebra construction *** 09:20 Please consider joining the LinkedIn group "Pre-University Geometric Algebra" Link to the pdf of the solution: https://vixra.org/abs/2404.0116 LinkedIn group, "Pre-University Geometric Algebra": https://www.linkedin.com/groups/8278281/ GeoGebra website https://www.geogebra.org/

To solve this problem, we use Geometric Algebra's outer product in two ways: To find the intersection of two lines, and to express the areas of triangles. The pdf of the solution is available at https://vixra.org/abs/2403.0027 Original problem from YouTube channel "Mind Your Decisions": https://www.youtube.com/watch?v=JRqkPE8ew40 LinkedIn group "Pre-University Geometric Algebra" https://www.linkedin.com/groups/8278281/

UPDATE: Amazingly, one FE debunker has claimed that "The Chinese aren't accused of covering up the origins of COVID." See screenshot #5 below, of the thread that was started a few days ago by a thoughtful YouTuber named DeeGee321 in the comment section of Sabine Hossenfelder's video "Flat Earth 'Science' -- Wrong, but not Stupid" (https://www.youtube.com/watch?v=f8DQSM-b2cc&t=0s). The assertion that China isn't accused of a cover-up is only one example of how uninformed my fellow debunkers are about this issue. I'm disappointed at how stubbornly some debunkers resist examining the documentary evidence, and (after finally examining it) how untruthful those debunkers are about that evidence; about the "Proximal Origin" article; and about Professor Ebright himself. Timestamps in screenshots shown below refer to times in the present video (i.e, mine). Note: At 8:12, I meant to say "indisputable" rather than "undisputed". The link for Nature Medicine's "Proximal Origin" article: https://www.nature.com/articles/S41591-020-0820-9 Unethical conduct of Peter Daszak: "Peter Daszak, Who Sought U.S. Funds for Wuhan Lab and Aided Cover-up, Faces Calls to Quit" https://www.newsweek.com/peter-daszak-u-s-funds-wuhan-institute-virology-aided-cover-faces-calls-quit-ecohealth-alliance-1636103 Calls to retract Natures article on proximal origin: Article that contains the link to Prof. Ebright's tweet: https://www.aier.org/article/caught-red-handed-scientists-call-for-full-retraction-of-natures-proximal-origin-paper-as-fraud-accusations-mount/ ‘Caught red-handed’: scientists call for complete retraction of Nature’s [proximal origin] document as fraud allegations mount" https://biz.crast.net/caught-red-handed-scientists-call-for-complete-retraction-of-natures-near-original-document-as-fraud-allegations-mount/ Contains images of Slack messages: https://theintercept.com/2023/07/21/covid-origin-nih-lab-leak/ Professor Ebright's profile at Rutgers University: https://www.waksman.rutgers.edu/ebright/people/dr-richard-h-ebright Prof. Ebright's tweet: https://twitter.com/R_H_Ebright/status/1682786904159182848 List of Slack statements by authors of proximal-origin-paper https://docs.google.com/spreadsheets/d/1znhGgzdbZZ7ZK3J5JMyUBHYi8ZGNGvM9cLdUvQq4YzA/edit#gid=0 Screenshots of the thread that was started by DeeGee321: (1) https://drive.google.com/file/d/1hCF55cxzHos-d02wwjvGA1KTXsctxfqt/view (2) https://drive.google.com/file/d/1ajIpeVNP3K63hQNleUzODJ9ZxT0KlDmD/view (3) https://drive.google.com/file/d/1IKSmIPdTE7gc3vvWIrjXzHMRLmx9Fn53/view (4) https://drive.google.com/file/d/12ChxUMRTXuaZVhVklmGmlBcw0U5yksDm/view (5) https://drive.google.com/file/d/1rH7sAxf5q3l1GINRAe0eKdSEQG1RJitD/view Screenshot of YouTuber "flook" 's dismissal of the documentary evidence without having examined it: https://drive.google.com/file/d/1vzRczYczpTIVrLPqWv9GAwcJ6CM3iOJi/view Additional sources: Additional documentation and discussion of Slack messages: • Matt Taibbi SLAMS Dems For Abandoning Free Speech At RFK Jr Hearing, MSM STILL Dismissing Lab Leak https://www.youtube.com/watch?v=AJqEGBZ56UU Glenn Greenwald:" • Smoking Gun New Proof Biden Admin Coerced Facebook Censorship" https://www.youtube.com/watch?v=J0GzHJTcdKE&t=28s

Handling "Rejections" is only one of many uses of GA's outer product. Here, to find the center and radius of a triangle's incircle, we use several ways of conceiving the outer product. 00:00 Introduction 00:29 Some of the ideas that we will use 01:15 The "rejection" of one vector with respect to another 05:38 Exploration/analysis of the problem 06:35 Our strategy 06:54 Formulation in terms of vectors 07:41 The first of our two simultaneous equations 08:39 The second of our two simultaneous equations 10:26 The result, and a small finesse 11:30 The group "Pre-University Geometric Algebra" Article: Location and Radius of a Triangle's Incircle Via Geometric Algebra https://vixra.org/abs/2306.0024

Here's what I found recently when I took a Flat Earther up on his boast that if I made accurate measurements on a physical globe, I would find that Con Man Dave Weis's so-called "globe route" between Beijing and Dallas is shorter than the great-circle route. Videos with Dave Weis's "globe route": • Stew Peters with Flat Earth Dave https://www.youtube.com/watch?v=b6nnmJaA-eg • Shiaswordgirl VS Flat Earth Dave! https://www.youtube.com/watch?v=YesCj2o9mto My video on which the boastful Flat Earther posted in Dave's defense: • Flat Earther Dave Weiss's "Flight Routes" Con Job https://www.youtube.com/watch?v=BCj45T219hU

Dave Weiss's fans will see how easy it is to prove that he's a con man. Links, in order of appearance: Video "Stew Peters with Flat Earth Dave" https://www.youtube.com/watch?v=b6nnmJaA-eg Video "Shiaswordgirl VS Flat Earth Dave!" https://www.youtube.com/watch?v=YesCj2o9mto Great-circle map showing Beijing-Dallas and Beijing-Calgary routes: https://www.greatcirclemap.com/globe?routes=PEK-DFW%2C+PEK-YYC Finding great-circle routes by stretching a string on a globe: https://aerosavvy.com/great-circle-routes/

00:00 Introduction 01:22 Formulating the problem in vector terms 02:52 It's now a simple vector-triangle problem 03:44 Solving the vector-triangle problem via GA's "outer product" 04:22 (For beginners) The detailed algebraic steps 05:55 The final answer 06:20 Please consider joining the LinkedIn group "Pre-University Geometric Algebra" Link to the "Mind Your Decisions" video: https://www.youtube.com/shorts/xmiJTy... LinkedIn group "Pre-University Geometric Algebra": https://www.linkedin.com/groups/8278281/

00:00 Introduction 01:22 Formulating the problem in vector terms 02:52 It's now a simple vector-triangle problem 03:44 Solving the vector-triangle problem via GA's "outer product" 04:22 (For beginners) The detailed algebraic steps 05:55 The final answer 06:20 Please consider joining the LinkedIn group "Pre-University Geometric Algebra" Link to the "Mind Your Decisions" video: https://www.youtube.com/shorts/xmiJTy... LinkedIn group "Pre-University Geometric Algebra": https://www.linkedin.com/groups/8278281/

00:00 Introduction 00:34 Two key ideas 01:09 Reducing the problem from "three spheres" to "two spheres and a point" 01:52 Our strategy 02:05 Formulate the "reduced" problem in GA terms 03:31 Essential: Obtain expression for the outer product of the projections 04:15 A difficulty 04:36 Looking for an idea: The geometric representation of bivector addition 05:15 A surprising simplification! 06:40 A change in our strategy 07:15 The answer, and its geometric interpretation 09:15 An extension to a more-general case 09:25 Please consider joining the group "Pre-University Geometric Algebra" Link for the document: https://vixra.org/abs/2210.0104 LinkedIn group "Pre-University Geometric Algebra" https://www.linkedin.com/groups/8278281/

Link to the Rolling Stone story, dateline 18 October 2022: "FBI Raids Star ABC News Producer’s Home [on 27 April]. Emmy-winning producer James Gordon Meek had his home raided by the FBI. His colleagues say they haven’t seen him since." https://www.rollingstone.com/politics/politics-features/fbi-raid-abc-news_producer-1234613619/

At 01:55, we'll see a specific, numerical example. 00:00 Quick review of GA equations for lines and planes 00:45 Formulating the equation that we need to solve 01:26 Solving the equation 01:55 A specific, numerical example 04:47 Checking the solution geometrically via GeoGebra LinkedIn group "Pre-University Geometric Algebra" https://www.linkedin.com/groups/8278281/

A worked, numerical example begins at 03:29. GeoGebra (https://www.geogebra.org/) is a fantastic, free tool that's fantastic for checking solutions that we derive via GA. Here, we learn the few, simple steps that let us identify the orthonormal components of bivectors by using GeoGebra's built in tools. 00:00 Introduction, and what's meant by the "orthogonal components of a bivector". 01:00 Why is GeoGebra so useful for learning GA? 01:47 The key idea that makes it simple: The duality relation v=B(I3)^(-1) 03:29 Get Real! -- a worked, numerical example. 07:22 Does our answer make sense? Note that the sum of the squares of the b's is 1. 07:51 What happens when we change the basis vectors e1, e2, and e3? 09:00 Please consider joining the LinkedIn group "Pre-University Geometric Algebra" (https://www.linkedin.com/groups/8278281/)

We will simplify the product e2e1e2e3, and show that the result is the unit bivector (e3e1) to which the unit vector e2 is perpendicular. LinkedIn group "Pre-University Geometric Algebra" https://www.linkedin.com/groups/8278281/

At 2:00 and thereafter, the equation for v should read "v=[p ∧ B]B^(-1). 00:00 Introduction, and the two cases that we'll consider. 00:45 A key idea: Rejection of a vector with respect to a bivector. 01:22 The 1st Case: Plane passes through a specified point, and is parallel to a given bivector. 01:51 The 2nd Case: Plane is at a given distance from a specified point, and is parallel to a given bivector. 03:41 Transforming the equation that we obtained for the 2nd case. LinkedIn group, "Pre-University Geometric Algebra": https://www.linkedin.com/groups/8278281/

Big-name Flat Earthers have appointed themselves to tell the rest of us what science is, and how to do it, even though FEs as a group have made no Flat-Earth-based contributions to science in the last 100+ years. Here's a chance for those FEs to redeem themselves by demonstrating the supposed superiority of their approach to understanding our world, by using their gravity-denying 'physics' to make accurate quantitative predictions about what will happen in simple situations. The previous video:

Because I expect Biden's apologists to attempt to deflect by raising the subject of January 6th, I'll say only that (1) some of the Jan 6 protesters were indeed acting criminally, and (2) I concur with self-defense expert Andrew Branca, that the police shooting of protester Ashley Babbitt, though tragic, was legally justified:https://legalinsurrection.com/2021/09/law-of-self-defense-analysis-jan-6-shooting-of-ashli-babbitt-was-legally-justified/ .

The solution per se starts at 03:55 . Mentioned at 08:30 -- LinkedIn group "Pre-University Geometric Algebra": https://www.linkedin.com/groups/8278281/ Link to the paper that's introduced in this video: https://vixra.org/abs/2208.0049 For Background on Rotations and Use of Geometric Products: "Rotate a Vector to a Specified Distance from a Given Point" https://www.youtube.com/watch?v=ErDTBNRyvvg "Skew lines, or Intersecting? Find out via Geometric Algebra" https://www.youtube.com/watch?v=cjARpnceRR8 Playlists: "Geometric Algebra for High Schoolers" https://www.youtube.com/playlist?list=PL4P20REbUHvzPW8rkHVyu9l20fJ5Iih2M "Geometric Algebra of Clifford, Grassman, and Hestenes" https://www.youtube.com/playlist?list=PL4P20REbUHvwZtd1tpuHkziU9rfgY2xOu

To demonstrate how to use the outer product to eliminate variables in simultaneous vector equations, we find the intersection of two lines, and detect when lines are skew. LinkedIn group "Pre-University Geometric Algebra": https://www.linkedin.com/groups/8278281/ . Playlist: "Geometric Algebra for High Schoolers": https://www.youtube.com/playlist?list=PL4P20REbUHvzPW8rkHVyu9l20fJ5Iih2M .

Train your "GA eyes" by deriving a simple, readily interpretable formula for rotating a vector so that its endpoint is at a specified distance "d" from a given point "P". Link to the document that presents three solutions: https://vixra.org/abs/2207.0169 https://drive.google.com/file/d/1QPR-917yr20ZkSn-TVDvibwVNdbTADcK/view?usp=sharing . LinkedIn group "Pre-University Geometric Algebra": https://www.linkedin.com/groups/8278281/ . Playlist "Geometric Algebra for High Schoolers": https://www.youtube.com/playlist?list=PL4P20REbUHvzPW8rkHVyu9l20fJ5Iih2M .

Remarkable, even for those two shameless charlatans! See also "Peter and Pete's Disinfo Endangers Viewers" ( https://www.youtube.com/watch?v=wGqDkbRXJPU ).

For once, Peter and Pete are truthful about their channel's contents. Here is the link to the scan, in searchable pdf form, of Cavendish's presentation of his gravity-measurement results to the Royal Society: https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1798.0022 . Pre-1900 replications of the Cavendish experiment: https://www.academia.edu/2524605/The_Cavendish_experiment_as_a_tool_for_historical_understanding_of_science Video: "To Flat Earth 'Physicists': A Challenge" https://www.youtube.com/watch?v=r7U58sZU6Bk Video: "Flat Earthers "Peter and Pete" Endanger Viewers with Disinfo" https://www.youtube.com/watch?v=wGqDkbRXJPU

Se aclarán dudas acerca de los términos, y se identifica el límite de una expresión compleja mediante varios temas claves. Un documento que demuestra los teoremas, y resuelve el límite que se trabaja en este video: https://drive.google.com/file/d/1rJifCU2WKpk3hZ1Pg1KM3HmpYm7ygwat/view?usp=sharing

Because I expect Garland's apologists to attempt to deflect by raising the subject of January 6th, I'll say only that (1) some of the Jan 6 protesters were indeed acting criminally, and (2) I concur with self-defense expert Andrew Branca, that the police shooting of protester Ashley Babbitt, though tragic, was legally justified: https://legalinsurrection.com/2021/09/law-of-self-defense-analysis-jan-6-shooting-of-ashli-babbitt-was-legally-justified/ . Link regarding anarcho-tyranny: https://im1776.com/2022/03/18/anarcho-tyranny/ . Regarding 18 USC 1507: https://www.govregs.com/uscode/title18_partI_chapter73_section1507 "Whoever, with the intent of interfering with, obstructing, or impeding the administration of justice, or with the intent of influencing any judge, juror, witness, or court officer, in the discharge of his duty, pickets or parades in or near a building housing a court of the United States, or in or near a building or residence occupied or used by such judge, juror, witness, or court officer, or with such intent uses any sound-truck or similar device or resorts to any other demonstration in or near any such building or residence, shall be fined under this title or imprisoned not more than one year, or both."

A sorpresa de muchos alumnos, los más de los gráficos NO SON planos cartesianos. Para poder usar con provecho las derivadas, etc. es importante conocer las diferencias.