In this video I go over a brief History lesson on Bezier Curves and show the people behind this amazing math concept as well as those that popularized it. Bezier curves are used widely in computer-aided design (CAD) in many industries, such as in design cars to even designing the fonts and letters that you view on your computer. In my earlier videos I went over a pretty cool “Laboratory Project” on Bezier curves and illustrated the properties of a cubic Bezier curve, so make sure to watch those videos. And usually whenever I go over videos on particular equations or math equations, I like going over the history of the brilliant mathematicians that pathed the way in developing these concepts, that quite frankly many people take for granted. The Bezier curves were popularized by the French engineer Pierre Bezier in which he used while working for the car manufacturing company Renault through his increasing leadership role in the use of mathematics in computer-aided modeling. While Pierre Bezier popularized the curves, he did not in fact discover them. The actual founder was Paul de Casteljau, a French physicist and mathematician, but he did not formally publish his findings. Nonetheless he has been acknowledged even by Pierre Bezier for having missed out on the fame that he rightly deserved for his findings. The Bezier curves remain still widely used in Computer-Aided Design as well as many other applications, so it is important to sit back and acknowledge the people that have brought this to the forefront. To illustrate an example of the Bezier curves, or Bezier surfaces for 3D shape, I also show a video of the Bezier Surfaces being used in the 3D modeling software, Sketchup. Three-Dimensional modeling, as well as many other applications are just the small sample of the usefulness of the Bezier curves, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhudIKXoMdwI5yK6oxg View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-bezier-curves-a-brief-history Related Videos: Laboratory Project: Bezier Curves Part 5: https://youtu.be/fwVaoM5PkN8 Laboratory Project: Bezier Curves Part 4: AMAZING Calculator: https://youtu.be/Kvb5yurofNo Laboratory Project: Bezier Curves Part 3: https://youtu.be/MzsT3FzrkU0 Laboratory Project: Bezier Curves Part 2: https://youtu.be/HN-xNfncklU Laboratory Project: Bezier Curves Part 1: https://youtu.be/S7aApca_B04 Parametric Calculus: Surface Area Part 1: https://youtu.be/4bMEIf6WD8M Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE Parametric Curves: ... https://www.youtube.com/watch?v=8aYVP_pdyZ8

In #911Truth Part 25, I have uploaded the full 9-1-1 phone call from Melissa Doi inside the impact zone at the 83rd floor of the South Tower on 9/11. The phone call shows a frantic Melissa saying "she can't breathe" and she is feeling intense heat but with very little indication of actual conventional thermal heat. She says she is "burning up" but she does not appear burned. She says there is smoke blocking out all the air, yet she hardly coughs and her voice is never hindered. She says she can't see fire but only that she can "feel" fire. The New York Police Department (NYPD) 9-1-1 emergency dispatcher tries to console her for over 20 minutes, and finally Melissa ends up "unconscious and snoring"; literally 18 minutes before the South Tower's fall. The World Trade Center 2 (WTC 2) or the South Tower was struck by an alleged plane 14 minutes before Melissa's phone call and between the 77th and 85th floors. Melissa was quite literally in the middle of the impact zone on the 83rd floor. She was with 5 other people trapped on the floor and even says she heard other people walking around, which may have been the Firefighters that quite literally walked up all the way up the alleged "flaming inferno". From the phone call, it is clear that Melissa did not experience heat from a fire, but rather something more subtle, such as possible microwave directed energy. This is inline with what the "jumpers" may have experienced as they took their clothes off while on the window edge before either throwing themselves or being launched against their wills. Here are some important links for reference: - Melissa Doi Wiki: https://en.wikipedia.org/wiki/Melissa_Doi - I downloaded the phone call from NPR: https://www.npr.org/templates/story/story.php?storyId=5658516 - I found portions of the beeped out audio from Metro.co.uk: https://metro.co.uk/2022/09/11/9-11-the-haunting-last-calls-from-victims-of-the-september-11-attacks-2-17345144/ - I used most of this phone call transcript: https://en.wikisource.org/wiki/9/11_Dispatcher_transcript - Articles about Melissa Doi: - 2006 New York The Sun: https://web.archive.org/web/20080907020542/http://www.nysun.com/editorials/melissa-doi/38055/ - 2006 Daily News: https://www.nydailynews.com/2006/08/17/i-feel-like-im-dying/ - 2006 The Washington Post: https://www.washingtonpost.com/archive/politics/2006/08/17/more-voices-from-911-im-going-to-die-arent-i/d99eba25-43df-4ae6-82c4-f3268a603123/ The timestamps of key parts of the video are listed below: - WTC 2 impact at 9:03:02 AM between the 77th and 85th floors: 0:00 - Melissa Doi calls 911 at 9:17 AM from the 83rd floor, she was with 5 other people: 0:36 - "We can't breathe", "it's very hot": 1:18 - "but no fire, right?" 2:25 - "I think there is fire" 2:44 - "you see no fire": 2:49 - "I don't see any air anymore": 2:58 - "I'm burning up": 3:30 - "We hear voices! HELLO! HELP!: 3:50 - "I feel like I'm dying": 4:39 - Court order removed civilians and Melissa Doi's voice from the remainder of the call: 5:02 - "I feel fire": 7:18 - Melissa Doi requests a note to her mother Evelyne Alderete: 7:59 - "Tell her that she's the best mom in the world... I love her with all my heart and soul": 8:54 - "Tell her I love her so much. I love her. She's the best mother a person could ever have": 9:13 - "Melissa, Melissa, Melissa..." 12:08 - "They sound like they might be unconscious": 22:23 - "Everybody's snoring": 24:15 - It's not dead there. They're snoring": 24:22 - "sounds like they were unconscious and snoring": 24:56 - "The line is now dead.... oh my Lord": 25:06 - MES Note: Melissa Doi experienced a different mechanism other than a conventional fire: 25:31 - WTC 2 South Tower falls at 9:59:00 - WTC 1 North Tower turning to dust (45X speed): 26:21 Stay tuned for #911Truth Part 26... - HIVE video screenshots: https://peakd.com/hive-113182/@mes/911truth-part-25-melissa-doi-911-call-from-the-83rd-floor-of-the-south-tower 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 . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=3inx6WvIEsg

In this video I go over unit vectors, which are vectors of length 1. Any vector "a" can be expressed as a unit vector "u" pointing in the direction of "a" by dividing the vector "a" by the length |a|. This produces an unit vector with length 1, which I also go over a simple proof that this is indeed the case. I also go over an example in calculating the unit vector of a given vector. The timestamps of key parts of the video are listed below: - Unit Vector Definition: 0:00 - Proof that the Unit Vector Length Equals to One: 2:22 - Example 6: 4:28 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 . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=OwwaSGTMJkM

In this video I make use of the extremely powerful mathematical search engine and computational database of Wolfram Alpha and basically show how it can provide you with all the steps in solving for the integral of a function, even very very complex ones. Download the notes in my video: https://www.dropbox.com/s/yskcnw2uogyksir/164%20-%20Step-by-Step%20Integrals%20Wolfram%20Alpha.pdf Related Videos: Graphing with the Google Search Part 1: http://youtu.be/1k3QDg2sB4o Graphing with the Google Search Part 2: Multiple Curves and Wolfram Alpha Comparison: http://youtu.be/jBThO3o1K3Y Google Graphing Calculator Part 3: 3D or Multi-Variable Graphing! AMAZING!: http://youtu.be/zQtcDvYxmGY Using Google Search as a Calculator: http://youtu.be/RxCqjklGw9A . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=jTcZZkloVWY