In this video I revisit the Tengri 137 Odin’s Triple Horn video that I made in my last video, and this time provide some further clarification, as well as correcting a few of the points that I had made in that video. First off, I made some mistakes in one of the matrix transforms that I showed in that video, and have since corrected it on the corresponding Excel sheet, but the overall video is still correct in that the Tengri 137 squares are simply made through matrix transformations. All that specific corrected matrix transformation only works in obtaining the Tengri squares 1, 3, 4, 5. To obtain the Tengri square 2 and 6, as discovered in my last video, we first need to rotate any of the other squares clockwise by 90 degrees. Also in this video, I illustrate visually what the Tengri squares represent, by graphing all of the numbers for each square, as well as comparing them with a square that I made by adding 158 to one of the distinct 4x4 perfect squares. This visual representation shows that the Tengri squares are simply transformations of my square, by moving numbers in groups of four the left and to the right of the center of the series of numbers. This is likely the basis for the Tengri 137 puzzle makers, and shows that the makers of these puzzles are very talented (and likely bored) mathematicians. I developed an Excel sheet to show this, and you can download and play around with it. I also included in it a simple “Magic Matrix Manipulator #MMM” which uses a “magic zero matrix transformation” that is a perfect square that all sum up to zero. This means that we can add this matrix to any other matrix to manipulate the numbers, without having to affect the current magic constant, in our case 666. In later videos I will look to derive the origins of the 3 distinct 4x4 perfect magic squares, so stay tuned for that! Also note that we can use any of these 3 distinct squares to obtain the Tengri squares. These distinct squares are just in the simplest form that can be written, not counting rotations, etc. Also, there are some more amazing and cool mathematics puzzles in the Tengri 137 documents, so I will research more into them to see if I can solve them. Whether Tengri 137 is made by aliens, or very talented (and bored) mathematicians, they are nonetheless very cool math puzzles and calculations, and are pretty fun to analyze and solve them! So stay tuned for my later videos! Download the notes in my video: Written Notes: https://1drv.ms/b/s!As32ynv0LoaIhusu7DlcCEHj6qha2A Excel Notes: https://1drv.ms/x/s!As32ynv0LoaIhutbP-FTgMxOa2f-pQ View video notes on the Hive blockchain: https://peakd.com/@mes/video-notes-tengri137-part-3-tengri-137-odin-s-triple-horn-visual-representation Related Videos: View the Full #Tengri137 Series: https://mes.fm/tengri137-playlist ?#Tengri137 Part 5: EPIC Intergalactic Battle: @666ab731 vs. @MathEasySolns: https://youtu.be/6hB7Xj5B5ls ?#Tengri137 Part 4: Tengri 137: Odin’s Triple Horn: Calculator + AMAZING MES "Sigma" Symbol: https://youtu.be/iXYehXgSUVQ ?#Tengri137 Part 2: Odin’s Triple Horn: Most Perfect “Diabolic” Magic Squares: https://youtu.be/4V9NVCMvoyI ?#Tengri137 Part 1: "Magic" Cubes Calculator + Linear Algebra Matrix Tutorial: https://youtu.be/3YxmH6ATD-k . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy 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

In this video I show that the dot product can be utilized to write any vector in the form of its direction angles and direction cosines. Using the geometric interpretation of the dot product from my earlier video, I show that each component of a vector is equal to the cosine of its direction angle. Note that direction angles are the angles that a vector makes with each of the x, y, and z axes. I also go over an example in calculating the direction angles. The timestamps of key parts of the video are listed below: - Direction Angles and Direction Cosines: 0:00 - Example 5: 14:32 This video was taken from my earlier video listed below: - Vectors and the Geometry of Space: The Dot Product: https://youtu.be/9uqtIk5iHys - Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product - Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GbHgvpTY1mx61nTNO-Msl8 Related Videos: Vectors and the Geometry of Space Playlist: 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=yuBhap9cgj0

In this video I go over a quick derivation of the hyperbolic trig identity sinh(x – y) = sinh(x)cosh(y) – cosh(x)sinh(y). The derivation simply uses my past work on the proof for sinh(x + y) = sinh(x)cosh(y)+cosh(x)sinh(y) and simply replaces y with -y. Thus using the definitions of sinh and cosh I show that cosh(-y) = cosh(y) and sinh(-y) = - sinh(y). Thus the only that changes when compared to the sinh(x+y) identity is we subtract instead of add the two terms together. This is a simple and quick derivation but shows the importance of building up previous work, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvwoBncxK428IJFN0Q View Video Notes on Steemit: https://steemit.com/mathematics/@mes/3xyhuv-video-notes-hyperbolic-trigonometric-identity-sinh-x-y Related Videos: Hyperbolic Trigonometric Identity: sinh(x+y): https://youtu.be/CtBzwqd4Rqc Hyperbolic Trigonometric Identity: cosh(x-y): https://youtu.be/GMGaQTym4d4 Hyperbolic Trigonometric Identity: cosh(x+y): https://youtu.be/B_rfrnhx-t4 Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc Hyperbolic Trigonometry Identity Proof: sinh(-x) = -sinh(x), cosh(-x) = cosh(x): http://youtu.be/-Wqq4Wzi7O8 . ------------------------------------------------------ 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=C1Vx3DaM0ig

In this video, I provide a quick review of the history behind Planck's Law, the formula derived by Max Planck in 1900 to resolve the Ultraviolet Catastrophe for blackbody radiation. The classical theory for blackbody radiation, proposed by John William Strutt (3rd Baron Rayleigh) and James Jeans, predicted that the energy emitted by a blackbody would increase without bound as the wavelength decreased, leading to a divergence at short wavelengths. This was wildly inaccurate, as experiments showed the energy spectrum peaks at a certain wavelength and then decreases at both higher and lower wavelengths. Through a process of careful analysis, Max Planck derived a formula that matched experimental results by assuming that a hypothetical electrically charged oscillator in a cavity containing blackbody radiation can only emit energy in discrete quantities, or quanta. This was a significant departure from the previous theory of continuous energy intervals. Planck's revolutionary assumption of quantized energy emission pioneered the development of modern quantum mechanics. Timestamps: - Planck's Law describes spectral density of electromagnetic radiation of a black body at thermal equilibrium: 0:00 - 1900, Max Planck proved that a hypothetical electrically charged oscillator can only change its energy in increments: 0:51 - The Law: Spectral emissive power per unit area, per unit solid angle for particular radiation frequencies: 1:48 - Increasing temperature increases total radiated energy and peaks at shorter wavelengths: 2:21 - Planck's Law formula: 2:41 - Graph of Comparison between Planck's Law vs Classical Theory (Rayleigh-Jeans Law): 3:34 - Solid angle (units in steradians) is angle of projection for a specific area on the surface of a sphere: 4:16 - Solid angle is used to quantify amount of radiation projected from a heat source: 4:49 - Note that Wikipedia uses various versions of Planck's Law: 5:18 - Rayleigh-Jeans Law formula (classical theory): 5:34 - Rayleigh-Jeans Law formula in terms of frequency: 6:22 - Ultraviolet Catastrophe: Rayleigh Jeans-Law strongly disagrees at short wavelengths: 6:43 - Planck's Law formula as energy density: 7:17 - Planck's Law and Rayleigh-Jeans Law formulas (used in my Calculus book): 7:44 - Planck's Law and Rayleigh-Jeans Law formulas as energy density in terms of frequency: 8:32 Full video and playlists: - Full video: https://youtu.be/oJpwidXu9Ps - HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars - Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb - Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz . ------------------------------------------------------ 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