Math Easy Solutions

If you have math related questions, I may have answers. April 23, 2025 Wednesday at 10:00 AM PST #math #coldfusion #LENR #FreeEnergy #nuclear Summary: SOON MES Math Q/A playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F1GgkU63uA9NIncxDS2q0- All Streams: https://www.youtube.com/@mes/streams . 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: [email protected] 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 This stream is created with #PRISMLiveStudio

In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and spiral. Although the Fibonacci sequence was named after the 12 century Italian mathematician Leonardo Bonacci, the Fibonacci numbers themselves appear to have first risen in 200 BC. Fibonacci never connected the sequence to the golden ratio, and it wasn't until the 17th century astronomer and mathematician Johannes Kepler that discovered that the limit of the ratio of consecutive Fibonacci numbers approaches the Golden Ratio. The golden ratio and Fibonacci sequence is seen throughout nature and in human art, design, and manufacturing. The Golden spiral, and its approximate Fibonacci spiral, is of particular prominence throughout nature. #math #fibonacci #goldenratio #calculus #sequences Timestamps: Life of Leonardo Bonacci aka Fibonacci (1175 to 1240-50 AD): 0:00 Fibonacci wrote Liber Abaci (Book of Abacus or Book of Calculation) in 1202 and popularized Hindu-Arabic numerals in Europe: 2:50 Fibonacci detailed how the Hindu-Arabic numerals can be used in accounting, finance, converting different currencies, and accounting: 4:48 Fibonacci's rabbits problem gave rise to the Fibonacci sequence: 5:55 Fibonacci sequence and its relationship with the Golden Ratio: 7:35 Fibonacci square tiling is an approximation to the Golden Spiral: 9:11 Fibonacci numbers first arose in 200 BC: 10:20 Fibonacci numbers are the sums of the shallow diagonals of Pascal's triangle: 12:17 Golden ratio = 1.6180339887... = ratio of two numbers is the same as ratio of their sum to the larger quantity: 13:09 Line segments in the golden ratio, and golden rectangle: 15:57 Golden ratio is the limit of the ratio of successive terms of the Fibonacci sequence, as originally shown by Kepler: 17:29 Ratios of Fibonacci numbers alternate greater and lesser than Golden Ratio phi: 19:30 Golden angle = 137.5077 degrees = 2.39996 radians = is the smaller angle of a golden circle: 22:47 Golden angle in some flowers: 25:00 Golden Spiral gets wider every quarter by a factor of phi: 25:27 Golden and Fibonacci spirals in nature, art, design, corporations, and advertising: 27:05 Golden spiral in pineapples, eggs, continents, Mona Lisa painting, Sonic the Hedgehog, website designs, movie posters, Apple logo, hurricanes, galaxies. Fibonacci numbers in tree branches. Trump golden spiral hair LOL: 31:53 Notes and playlists: Summary: https://inleo.io/threads/view/mes/re-leothreads-2vkmxoa5s Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more Infinite 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: [email protected] 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 go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo Bonacci, or more commonly known as Fibonacci (short for "filius Bonacci or "son of Bonacci"), first wrote the Fibonacci sequence in 1202 when analyzing the population growth of an idealized rabbit population. Assuming rabbits live forever, and starting with a pair of rabbits that reproduce another pair after 2 months of age, the population starts growing according to the Fibonacci sequence: the current population = the population 1 month ago + the population 2 months ago I then show that the limit of the ratio of consecutive terms of the sequence, (population at n + 1 month) / population at n month), is equal to the famous golden ratio. I go over the history and more instances of the Fibonacci sequence and the golden ratio in the next video! #math #sequences #fibonaccisequence #goldenratio #calculus Leonardo Bonacci: https://en.wikipedia.org/wiki/Fibonacci Fibonacci sequence: https://en.wikipedia.org/wiki/Fibonacci_sequence Timestamps: Exercise 4: Fibonacci problem about rabbit reproduction: 0:00 Solution to part (a): Recap on the Fibonacci sequence: 0:51 Solving the rabbit reproduction problem: 1:40 Writing down the sequence of new rabbit pairs being reproduced: 3:33 Sequence is just the Fibonacci sequence: 6:07 Solution to part (b): Ratio of the Fibonacci sequence terms: 6:40 Rewriting the sequence to plug in the Fibonacci sequence: 7:58 Proved our sequence recurrence relation: 10:00 Finding the limit of the sequence, using Theorem 2 (Exercise 1): 10:41 Solving the limit using quadratic formula: 13:36 Taking the positive value as our limit: 14:45 Our limit is actually the Golden Ratio! 15:23 Notes and playlists: Summary: https://inleo.io/threads/view/mes/re-leothreads-21jgbnz5x Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more Infinite 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: [email protected] 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 have condensed the earlier 1985 Jack Houck footage of the Hutchison Effect into a brief 5 minute video. I was able to capture many effects not noticed by Jack Houck, John Hutchison, or Alexis Pezarro. These effects, such as the entire back table slowly shifting horizontally and many small metal and aluminum foil pieces gradually moving, have literally never been observed for 40 years! Some of the effects require quite literally 1000X speed just to spot. The professional tripod filming of Jack Houck made this timelapse possible. Another important observation is that many effects occur at the instant of the high voltage capacitor spark gap discharge. Jack Houck also wrote up a report detailing the experiment and his observations, thus further making this one of the rarest and most important Hutchison Effect footage currently available! #HutchisonEffect #technology #timelapse #zeropointenergy #science Links to videos used and more info: Hutchison Effect hard drive: https://mes.fm/hutchison Videos are in the folders: 1980s Hutchison / 1985 5 hours of 1985 Jack Houck footage, and report: https://peakd.com/hive-128780/@mes/oqetactn John Hutchison Official YouTube @HutchisonEffect https://www.youtube.com/@HutchisonEffect Jack Houck report of the 2 day experiment and filming: https://1drv.ms/b/s!As32ynv0LoaIjb0IknXf_atQPtyrow George (Jack) Brandt Houck died March 26th, 2013 at the age of 74: https://youtu.be/D1pJp_CvjsQ Alexis Pezarro started Pharos Technology with John: https://hiroko.or.jp/wp-content/file/gravity-control/Space resonance/HutchisonEffect.pdf Jack Houck was from McDonnel Douglas and is famous for his spoon bending PK (psychokinesis or telekinesis) parties. https://en.wikipedia.org/wiki/McDonnell_Douglas https://youtu.be/D1pJp_CvjsQ https://en.wikipedia.org/wiki/Telekinesis Jack was contacted by Col. John Alexander and others to film the Hutchison Effect: https://snipboard.io/qsmLDv.jpg Jack Houck letters to John: https://1drv.ms/f/s!As32ynv0LoaIjbsw-0RZ3G1G_-ci_g Timestamps: Day 1: August 13, 1985 Jack Houck footage: 0:00 John Hutchison turning on the microwave generators: 0:10 John cranking up the power: 0:21 Spark gap discharge lightning strike: 0:40 Objects on the left of the back table start moving (163X speed): 0:42 Big brass bushing cylinder falls over: 0:55 Back table starts moving slowly backwards: 1:04 Table moves again, plus 5X replay: 1:27 Table moves again, plus 10X replay: 1:50 Aluminum foil moves to the left of the table (217X speed) and top part falls at instant of spark gap discharge: 2:08 Aluminum foil moves again to the left of the table (56X speed) and falls at instant of spark gap discharge: 2:16 Day 2: August 14, 1985: Metal piece moves to the left of the table then falls at instant of spark gap discharge, and other piece moves (245X speed): 2:34 Aluminum foil on brass bushing cylinder also moves. Heavy electromagnetic (EMF) camera interference: 2:50 Two Aluminum foil pieces move (143X speed), then both fall at instant of spark gap discharge: 3:10 Another aluminum foil piece moves (48X and 23X speeds), and each time moves more abruptly at instant of spark gap discharges: 3:19 More heavy EMF camera interference: 3:40 Many small metal pieces, magnets, and two aluminum foil pieces move slowly (911X speed), plus 1822X speed replay: 4:31 add extra arrow to aluminum foil Small metal piece moves slowly (141X speed), and replay at 423X speed: 4:54 More heavy EMF camera interference: 5:12 Final timelapse (323X speed): 5:36 Video screenshots and playlist: Screenshots: https://peakd.com/hive-128780/@mes/tznpkpee Hutchison Effect playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GlfVj5AYNtbF688pr8fk9X . 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: [email protected] 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

If you have math related questions, I may have answers. April 16, 2025 Wednesday at 10:00 AM PST #math #nasa #apollo #space #technology Summary: SOON MES Math Q/A playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F1GgkU63uA9NIncxDS2q0- All Streams: https://www.youtube.com/@mes/streams . 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: [email protected] 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 This stream is created with #PRISMLiveStudio

In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). I prove this using the precise definition of limits of general functions and sequences. This theorem is also expected since a function at a particular value is equal to the limit as x approaches that particular value; thus we are just replacing the x term with the infinite sequence. #math #sequences #limits #education #calculus Timestamps: Exercise 3: Theorem 3: Sequence inside a function: 0:00 Solution using the precise definition of limits: 1:27 f is continuous at L so limit is same as plugging in function: 3:45 Replace precise definition of a limit for a continuous function with the sequence: 5:54 Precise definition of the limit is the same for our sequence: 7:29 Notes and playlists: Summary: https://inleo.io/threads/view/mes/re-leothreads-2q1z3cwmj Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more Infinite 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: [email protected] 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 prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved this using both Squeeze Theorem and the precise definition of a limit. Using the squeeze theorem, I show that the minimum values that the sequence can be is the negative of the absolute values of its terms, and the maximum is the absolute values. Since both these sequences approach zero, our general sequence gets squeezed and is thus also zero. Using the precise definition of the limit of a sequence, I show that since the limit is zero, the condition that the difference between the absolute value of the difference between any term of the sequence and the limit simplifies to just the absolute value of the terms itself, which is thus identical for both the general sequence and the absolute value of the terms. Thus, both sequences are identical and equal zero. #math #sequences #absolutevalue #education #calculus Timestamps: Exercise 2: Theorem 2: Limit of absolute value of a sequence: 0:00 Solution 1: Squeeze Theorem: Limit is squeezed between positive and negative absolute values: 0:51 Solution 2: Definition 2: Precise definition of a limit: 2:37 Limit is zero so absolute value sign is identical to normal limit: 4:39 Theorem 2 is solved: 5:40 Notes and playlists: Summary: https://inleo.io/threads/view/mes/re-leothreads-bhuzhkpl Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more Infinite 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: [email protected] 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