Let me just say, THANK YOU! I have struggled with math for quite some time now, this year I am in geometry and I would try and try but could never even understand. This video and others on your channel made me understand! Thank you!
What kind of Physics teacher is gonna spend time to teach you how to calculate basic trigonometry? 😂You mf tripping. I doubt it's the teachers issue when you expect physics teacher to explain you elementary school concepts
Thank you so much. This helped me so bad. I don’t usually comment on videos but I felt the need to on this one. I struggle with math a lot and so I use TH-cam to help me all the time. A lot of the time, TH-cam helps and I learn. But I don’t remember ever being this interested in math before and I don’t remember learning so much in such a short period of time! You don’t understand how grateful I am for this. You have gotten yourself a new subscriber and I am so pleased to have found you Thanks for your help, I’m sure I’m not the only one who can agree
I have watched your channel since 8th grade, now I'm in the end of my sophomore year. It helps so much!! Thank you for the knowledge. I thought I would never understand a lot of things in math, but you've proven me wrong. Keep up the good work 👏 ❤
she writes on a window normally(with her right hand) and then whilst editing the video she also mirrors the whole video which looks like she is writing backwards, tequnically it's am illusion. ✌✋💅
Well, I was away for a while and missed several videos. I spent the first half of this year as a full-time volunteer algebra tutor at a local "continuation" high school, for students who weren't well-served by the regular system. All had failed algebra at least once, and most had failed entire years of school. Many had severe life stresses outside of school, with family, poverty and various drug dependencies and mental health issues. A number of them had jobs, and many were on the verge of aging out of the system. The first thing I learned is that, despite being a master of algebra, I didn't know a thing about teaching it. So, immersion in pedagogy was an initial task. The second thing I learned was that being able to teach algebra wouldn't magically enable these students to learn it. Most weren't in a state of mind or heart that was conducive to learning anything, much less something as abstract as algebra. The vast majority believed they had no math abilities, and the rest believed algebra had no practical role in their lives. With all this stacked against them, they then had to contend with the intense frustration and self-imposed humiliation they felt when they couldn't do a review problem they had been able to solve a year previously. The third thing I learned was that I had to start with these students where they actually were, and not where I thought or hoped they would be. That meant asking if they had slept the night before. Had eaten breakfast. Weren't too hot or cold. Felt well. Were hydrated. Weren't (too) high. The fourth thing I learned was that to find out where they were I had to become a powerful observer, a gentle questioner, a rock-solid presence for them, and find ways to create a space of safety and careful risk-taking. I had to do lots of work on myself. To learn to get close to students without going over the edge. To "love them to death" as one teacher put it to me, without killing myself. To be totally warm and open, yet keep a safe distance. I didn't have nearly enough successes, but damn if I didn't have some awesome ones! I remember one young woman who would do this low "Ohhhh" when she "got" something, and I remember watching her take a test where she did that twice, during the test! There was a very sullen young man who was always high (and a genuine ass of the first order), but who somehow agreed to come in straight enough to give algebra a serious try. He couldn't do any of the review problems, so I grabbed the prior text and went through it backwards. We got to the point where we found his problem was multiplication: He had forgotten how it worked, and had never memorized any multiplication tables. We started from there and made slow but steady progress. One day walking across the quad between classes, I saw him on the far side: He changed direction to come past me for a fist-bump. Two of his other teachers were also there and were shocked, nearly to the point of tears (as was I). It was the first time any of us had seen him have a positive self-directed interaction with any adult on campus! There were more victories like that, large and small. Then my savings started to run low, and I had to get another day job as a senior systems engineer. It's a great job, with a talented team working on cool products. But I find I'm in a bizarre state: I've never had a job I liked more and loved less. Because my heart isn't in it: What I want to do is teach! So I'm living on a fraction of my salary, saving money for tuition for my teaching credential, saving money to pay off my mortgage, and saving money so I can afford to live on teacher's pay in Southern California. To tell you the truth, the students who "get it" I'll turn over to you: They won't need me for much, and you've got that ASMR thing going. I want to work with students who think they have an allergy to math combined with existential dread and nightmares.
Beautiful experience. You are right, the first thing to tackle is their fear of math. When we get to high school we are told "you're going to see algebra uuuh" as if it were a demon. And then in university it is "calculus oooh so difficult". But we all have a brain capable of math. I blame said fear and the people that don't know how to teach, who just make students feel worse. Congratulations.
Interesting story. I was a mechanical designer for 35 years retired now became a Walmart Greeter. Big change for me. Im back at school now getting my degree in Arts for teaching. Im 67 now wish me luck.
I’m really glad I found your channel. You have a nice mix of simple math to calculus. Great for a refresher on many types of math. Nothing I love more than numbers.
Excellent run down. As a builder years ago I taught myself Trig to do more tricks with fancy roof rafters etc. That took me a couple of weeks to do what you did in 14 minutes.
I genuinely found this very helpful. Especially since I'm a visually impaired student so I struggle when teachers show things on a projector. Thank you
I've learnt this in secondary school 30+ years ago but never had to use it since, so have forgotten all about it. It's coming back with this video now.
Oh my goodness, thank you so much for this video. I have been struggling with one problem for the past 4 hours and this really helped a lot. The explanation of solving is very clear and understandable. Thanks again!
In 13 minutes you explained more than my teacher who took 2 weeks to explain it. I have a unit test tomorrow and this really helped! Thank you so much you explain this way better
Nancy, I started a channel not that long ago with intentional Math asmr videos, but I swear yours is unintentional ASMR! I haven't seen all of them, but you're doing good work. Also, somehow, YT thinks our channels are related lol, maybe because of MIT, but either way that's flattering to me, b/c you're great : )
wow!!! I'm in a trig class now and EVERYTHING that I have been trying to learn over the last two weeks was accomplished within the last 15 minutes!I Thanks!!
I swear these videos save my life! My math teacher is the type to just give you a print out of the notes and be like "figure it out!" so she reeeeally helps meee!!!!
I like her explanation better than any other I've seen, she dotted every I and crossed every t, she didn't speak to fast or to slow, I think I've found the Greatest math teacher on TH-cam. I met a math teacher in Lumberton, Mississippi who had the Pythagoras theorem tattooed on his leg. All builders and construction engineers need to know and understand this math if no other. Navigation on the oceans needs this math . It has to be one of the greatest math sciences in existence. But in all truth, she is the best at teaching this. I do now want to check out her other videos. One of my youtube channels is moseseseseses, I can't sign into it anymore because I lost my password, I teach French, Spanish, and Gregg shorthand on that channel. My other channel, mostly guitar playing, is my name, Joseph kingston.
TOA actually means toilet in Swedish. 😉 I've never gotten these sides in my thick skull... But why are we counting the corners of triangles counter clockwise?
Thank you so much. I have been looking everywhere on how to do this and I finally found answers. Since I am homeschooled I don’t find out how to do this during school but since you presented me with answers I can finally finish my work.
I could never have remembered SOH CAH TOA. I mean, what even is that? My sister told me a phrase that I still remember years later: Oscar Has / A Hairy / Old Ass.
Ma’am I have done trig three times, I think I just needed to learn it the way you explained it!!! I know how to solve a triangle now! I know I am dumb slow but this is monumental for me and my feelings!!!!! Thank you ma’am
Three angles and one side is easy. Since you recommend a calculator, the Law of Sines works great on this one. Sin A/a=SinB/b=SinC/c. "The hypotenuse of a right triangle equals the square root of the sums of the squares of the other two sides" : Scarecrow in the "Wizard of Oz". a2+b2=c2 is incomplete as you still need to do a square root function to obtain the answer. For ease, think 3-4-5. (3x3)+(4x4) is 9+16 = 25. The square root of 25 is 5, hence 3-4-5.
Ooof thank you! I was having a hard time understanding this topic but your way of explaining it is awesome! RIght now Im taking college pre calc but I was suprised to see that I watched this video back in High School for Algebra 2!
thank u so much for making this video! im rlly confused when it comes to sin, cos, and tan (specifically as to which one i should be using depending on the question) and u helped me so much! subscribed!
Random video teaching me math: “do you trust me?”
Me who has a test tomorrow: “with every fiber in my body.”
SAME I HAVE A QUIZ ON THIS TOMMORROW LMAO
I have my grade 10 final exam tomorrow and this is teaching me surprisingly well
Saaame bro
Plottwits you are made of cells not fibres
@@elihamilton5842 yo id be careful telling people your school name on youtube, even if it is in the comments of an educational video.
The fact that she writes backwards on a clear board is amazing
she probably writes normally, then mirrors the video.
I think they just mirror the video if not I tried it out that it's not that hard to write
It’s a mirrored video
Omg that's true I feel bad
Yea it is tuff
Let me just say, THANK YOU! I have struggled with math for quite some time now, this year I am in geometry and I would try and try but could never even understand. This video and others on your channel made me understand! Thank you!
Teachers are always telling me that Math is beautiful. Now, I get it.
UwU
Lol
*High five*
@@smithbennington4569 OwO
Helped a little but slow
video's comments:
5% thanks for the nice explanation
95% wow you're so beautiful
😂😂😂😂😂😂
Comment section needs to chill fr
can't really blame them
😂🤣😂🤣😂
Grow up.
POV: your here because you have hw and didn’t pay attention in class💀👍
You not wrong☠️☠️☠️
7
Actually im not paying attention *and i have test next week and im not ready*
@@ehe5419 yes l have exam today
@@ehe5419 a obaut a right treangle and algebraic exeprition
I learned more in the first 6 minutes than with 5 hours with my physics teacher.
Gerald Irvin really? Y’all gotta speak up
What kind of Physics teacher is gonna spend time to teach you how to calculate basic trigonometry? 😂You mf tripping. I doubt it's the teachers issue when you expect physics teacher to explain you elementary school concepts
Thank you so much. This helped me so bad. I don’t usually comment on videos but I felt the need to on this one. I struggle with math a lot and so I use TH-cam to help me all the time. A lot of the time, TH-cam helps and I learn. But I don’t remember ever being this interested in math before and I don’t remember learning so much in such a short period of time! You don’t understand how grateful I am for this. You have gotten yourself a new subscriber and I am so pleased to have found you
Thanks for your help, I’m sure I’m not the only one who can agree
Try to learn with your own teacher guys I ask her all the time
it has help me a lot.thank a lot and send ur number
@@famidaaliahmed7816 some teachers honestly dont know what they are explaining
Hiii maria
I agree with you, She is amazing in explaining ❤
She also puts her beauty in the equation. That’s a smart thing to do
I learned more in this 10 minute video than I did in 2 weeks in my math class. THANK YOU!
Nancy, great video, explanation beautifully. now learning a lot more than b4.
thank you.
Hi
Same here.
SAME
How are you?
How does she do this...my teacher explained this in the exact same way and I was buffering. I watched ½ of this and nailed the test...lol
@Kola Bright might be xd
Try my TH-cam channel “mathfullyexplained “. Full unit on rt tri trig.
@Kola Bright THIS was one of the most OUTSTANDING and ON-THE-POINT replies I have EVER SEEN!!
Can anyone help me with my hmw I watched a million vids n I still don’t understand shit ._.
I’d pay you tho $
@Kola Bright unrelated
I have watched your channel since 8th grade, now I'm in the end of my sophomore year. It helps so much!! Thank you for the knowledge. I thought I would never understand a lot of things in math, but you've proven me wrong. Keep up the good work 👏 ❤
Ok, the thing that impressed me the most is that she wrote everything mirrored
no she mirrored the video XD smh
Thats too complicated. its a mirror video
Bruh 🤣
same.
she writes on a window normally(with her right hand) and then whilst editing the video she also mirrors the whole video which looks like she is writing backwards, tequnically it's am illusion.
✌✋💅
Excellent explanation! I also like the “speed up” and “speed down” sound and visual effect. Well done!
FACTS BRO
The most gorgeous mathematician of all times
I am japanese, and I love math.
I found this beautiful teacher a while ago. Your voice is so confortable.I will continue to listen to you carefully.
Carefully?
Sugoi!
Comfortable*
Nani?
No offence
Thank you so much Nancy, i haven't done trig in over 20years. Your explanation was so great that i was able to remember .💯
The teacher: Wow all the boys aced the exam
Girls: ITS SO HARD
The boys: paying more attention than usual.
Ha got it
@GigaramsYT yea surface areas are hard D:
@Lisa Harper no need to get offended, its just a joke
@GigaramsYT 👁👄👁 i pretend i do not see
I mean its not only boys watching this because of a pretty lady 😳😳
Well, I was away for a while and missed several videos. I spent the first half of this year as a full-time volunteer algebra tutor at a local "continuation" high school, for students who weren't well-served by the regular system. All had failed algebra at least once, and most had failed entire years of school. Many had severe life stresses outside of school, with family, poverty and various drug dependencies and mental health issues. A number of them had jobs, and many were on the verge of aging out of the system.
The first thing I learned is that, despite being a master of algebra, I didn't know a thing about teaching it. So, immersion in pedagogy was an initial task.
The second thing I learned was that being able to teach algebra wouldn't magically enable these students to learn it. Most weren't in a state of mind or heart that was conducive to learning anything, much less something as abstract as algebra. The vast majority believed they had no math abilities, and the rest believed algebra had no practical role in their lives.
With all this stacked against them, they then had to contend with the intense frustration and self-imposed humiliation they felt when they couldn't do a review problem they had been able to solve a year previously.
The third thing I learned was that I had to start with these students where they actually were, and not where I thought or hoped they would be. That meant asking if they had slept the night before. Had eaten breakfast. Weren't too hot or cold. Felt well. Were hydrated. Weren't (too) high.
The fourth thing I learned was that to find out where they were I had to become a powerful observer, a gentle questioner, a rock-solid presence for them, and find ways to create a space of safety and careful risk-taking.
I had to do lots of work on myself. To learn to get close to students without going over the edge. To "love them to death" as one teacher put it to me, without killing myself. To be totally warm and open, yet keep a safe distance.
I didn't have nearly enough successes, but damn if I didn't have some awesome ones! I remember one young woman who would do this low "Ohhhh" when she "got" something, and I remember watching her take a test where she did that twice, during the test!
There was a very sullen young man who was always high (and a genuine ass of the first order), but who somehow agreed to come in straight enough to give algebra a serious try. He couldn't do any of the review problems, so I grabbed the prior text and went through it backwards. We got to the point where we found his problem was multiplication: He had forgotten how it worked, and had never memorized any multiplication tables. We started from there and made slow but steady progress. One day walking across the quad between classes, I saw him on the far side: He changed direction to come past me for a fist-bump. Two of his other teachers were also there and were shocked, nearly to the point of tears (as was I). It was the first time any of us had seen him have a positive self-directed interaction with any adult on campus!
There were more victories like that, large and small.
Then my savings started to run low, and I had to get another day job as a senior systems engineer. It's a great job, with a talented team working on cool products. But I find I'm in a bizarre state: I've never had a job I liked more and loved less.
Because my heart isn't in it: What I want to do is teach! So I'm living on a fraction of my salary, saving money for tuition for my teaching credential, saving money to pay off my mortgage, and saving money so I can afford to live on teacher's pay in Southern California.
To tell you the truth, the students who "get it" I'll turn over to you: They won't need me for much, and you've got that ASMR thing going. I want to work with students who think they have an allergy to math combined with existential dread and nightmares.
Beautiful experience. You are right, the first thing to tackle is their fear of math. When we get to high school we are told "you're going to see algebra uuuh" as if it were a demon. And then in university it is "calculus oooh so difficult". But we all have a brain capable of math. I blame said fear and the people that don't know how to teach, who just make students feel worse. Congratulations.
Number Line Nomad and the Duchess of Denominators have profound respect for your sincere dedication. Have a MatheMagical year!
good job.
@@lexinaut donald duck says thank you from mathmagic land.
Interesting story. I was a mechanical designer for 35 years retired now became a Walmart Greeter. Big change for me. Im back at school now getting my degree in Arts for teaching. Im 67 now wish me luck.
POV u haven’t done your homework and you have a test today
Lmao im taking my test rn
@@simonbrown4314 how did you do?
I’m really glad I found your channel. You have a nice mix of simple math to calculus. Great for a refresher on many types of math. Nothing I love more than numbers.
That moment when you already know everything Nancy explains but you watch anyway.
That moment when you know you are supposed to pay attention but still cannot manage.
Or understand nothing..
i clicked even though i already learned this a few mins earlier
Lilpat same 😂 but i’m still not 110% sure that i can get a 100 on my test!☹️
I know how to solve this 5 years ago but I'm still waiting 😍
i like this because she explains in very quick and simple terms while also showing what she’s doing in a visual and easy way.
I use your videos in my classroom often to supplement my own teaching. Thank you for doing what you do!
The way you pronounced "Pythagorean Theorem" and "emphasis for the syllables" got me laughing! Love it. This video was really helpful, thank you!
Istg I watch so many math vids but Nancy pi ALWAYS helps. Like fr she’s so clear and her videos help sm
Excellent run down. As a builder years ago I taught myself Trig to do more tricks with fancy roof rafters etc. That took me a couple of weeks to do what you did in 14 minutes.
Professor Nancy Pi, thank you for an outstanding video/lecture on Solving Right Triangles. This is an error free video/lecture on TH-cam TV.
I genuinely found this very helpful. Especially since I'm a visually impaired student so I struggle when teachers show things on a projector. Thank you
I've learnt this in secondary school 30+ years ago but never had to use it since, so have forgotten all about it. It's coming back with this video now.
Oh my goodness, thank you so much for this video. I have been struggling with one problem for the past 4 hours and this really helped a lot. The explanation of solving is very clear and understandable. Thanks again!
In 13 minutes you explained more than my teacher who took 2 weeks to explain it. I have a unit test tomorrow and this really helped! Thank you so much you explain this way better
Nancy, I started a channel not that long ago with intentional Math asmr videos, but I swear yours is unintentional ASMR! I haven't seen all of them, but you're doing good work. Also, somehow, YT thinks our channels are related lol, maybe because of MIT, but either way that's flattering to me, b/c you're great : )
This video helped me so much, I am honestly very grateful for you. You literally helped me get through lineman school. Thank you❤️
You’re seriously a blessing for making this so simple!
wow!!! I'm in a trig class now and EVERYTHING that I have been trying to learn over the last two weeks was accomplished within the last 15 minutes!I Thanks!!
Nancy got me through college years ago, she's my hero
I'm a Math Prof, but I'm binge watching Nancy's videos... for a friend. #science
Thank u so much for being my literal math teacher without being there your voice is so soothing and calm and supporting!
Your lessons have always been my go to. You make it so easy to follow. I sincerely appreciate you!
This helped me a ton! Thanks so much. Are you going to do a second video on inverse trig functions?
I got it! This was easier to follow than other TH-cam videos. Me old school builder this will save much work and time, thank you Nancy.
I really, really appreciate it (right on time), please cover more stuff on Trig if you have the chance.
I swear these videos save my life! My math teacher is the type to just give you a print out of the notes and be like "figure it out!" so she reeeeally helps meee!!!!
i like how she draws triangles super fast
I like her explanation better than any other I've seen, she dotted every I and crossed every t, she didn't speak to fast or to slow, I think I've found the Greatest math teacher on TH-cam. I met a math teacher in Lumberton, Mississippi who had the Pythagoras theorem tattooed on his leg. All builders and construction engineers need to know and understand this math if no other. Navigation on the oceans needs this math . It has to be one of the greatest math sciences in existence. But in all truth, she is the best at teaching this. I do now want to check out her other videos. One of my youtube channels is moseseseseses, I can't sign into it anymore because I lost my password, I teach French, Spanish, and Gregg shorthand on that channel. My other channel, mostly guitar playing, is my name, Joseph kingston.
Nancy, you make being geek so chic! Keep up the great work. You're a great help to my high school-age daughters.
Dave nice one Dave
If this was my teacher I’d have an A, not a D
😢😂
Thanks so much for this. You really helped my son who was struggling to understand the concept. He learnt this in just this one video!
OMG THANK YOU SO MUCH NO ONE IN THE ENTIRE WORLD CAN TEACH AS GOOD AS YOU
its been almost 10 years since Ive had to do this.. thank you for the refresher!
Who would like their teacher to be this gorgeous.
ok virgin
Me
ugggh men.... gosh where's the face palm emoji!!!!
@@snake9505 no prob if ur jealous lol
@@dhivyaradhakrishnan1179 I'm not being jealous its just weird when men do this ok. TPWK
thank you so much for this video!!! I have to present how to solve a problem like this in a few minutes and before this video i didnt know anything 💀💀
He fellow Exo l
5 year old me: *Draws a triangle*
My parents: *Cherish the triangle*
My math teacher: 1:05
I clicked on this video already knowing people are gonna say she's beautiful smh, TH-cam is just too predictable
same 🤣🤣🤣🤣🤣🤣🤣
No one heard her "emphasis on syllables" joke? It was a good one.
You are saving my life with the knowledge you teach I can be proud of myself
TOA actually means toilet in Swedish. 😉
I've never gotten these sides in my thick skull...
But why are we counting the corners of triangles counter clockwise?
I used to teach Mathematics and wish this girl was around to use her TH-cam videos. Pleasing on the eye too.
You are the best teacher of this stuff ever, and, if you allow me to say it, you are not only really smart but also beautiful.
4:33 She's in love
This is the goat of maths videos thank you so much
Nancy reminds me of a line in a movie I saw, "She's a brain!" . . ."Trapped in the body of a game-show hostess."
Subscribed to help my kid with her math homework as it is getting beyond my recollections from attending school. Nice lesson! Thanks so much!
Nancy : dont pronounce it pythagorean theorem
Also Nancy : sylAbbles
This actually one of the most helpful videos I’ve watched. Thank you
freshman year and this clears up everything now, thank you
Ohh man people say trigonometry is hard but when I see this video it made me love trigonometry 🤩🤩🤩.very nice vid . 👍👍Love it .
How’d you get into MIT? What was your high school gpa and act score?
Damn! If you were my math Teacher I would pay full attention 😍
Same!
I love you Nancy. You're the best teacher in algebra
a few years later and I was able to better understand and solve these kinds of problems, thank you!
Thank you. I understand you more than every maths teacher I’ve had.
Thank you so much. I have been looking everywhere on how to do this and I finally found answers. Since I am homeschooled I don’t find out how to do this during school but since you presented me with answers I can finally finish my work.
You’re a life saver, haven’t done this stuff since high school. It doesn’t hurt that you’re easy on the eyes either 😂
I wonder Why I payed attention the hole time 😂
almost 30 years out of school
but look at this brings back my day
Y'all been trying to figure out how she writes for the longest. People she just writes backwards it's not that deep
No she doesn't, she writes the right way around, she just reverses the picture horizontally
Oh yeah, I forgot how much I love watching trig tutorials!
I could never have remembered SOH CAH TOA. I mean, what even is that?
My sister told me a phrase that I still remember years later: Oscar Has / A Hairy / Old Ass.
O my god that's brilliant lol
or just remember the phytagorean theorem and sin 30°
Ma’am I have done trig three times, I think I just needed to learn it the way you explained it!!! I know how to solve a triangle now! I know I am dumb slow but this is monumental for me and my feelings!!!!! Thank you ma’am
She can teach me trig all day and all night long!!! She is so beautiful!
You're amazingly beautiful! . . . Oh, and an amazing math teacher
Just needed a reminder on how to find an angle. Thanks for making trig so easy.
she a baddie
Three angles and one side is easy. Since you recommend a calculator, the Law of Sines works great on this one. Sin A/a=SinB/b=SinC/c. "The hypotenuse of a right triangle equals the square root of the sums of the squares of the other two sides" : Scarecrow in the "Wizard of Oz". a2+b2=c2 is incomplete as you still need to do a square root function to obtain the answer. For ease, think 3-4-5. (3x3)+(4x4) is 9+16 = 25. The square root of 25 is 5, hence 3-4-5.
I’d like to solve her triangle.
i think were all forgetting the fact that at nancy's point of view she's writing every single one of that letter backwards/inverse
mad respect
Now let's solve for the missing ring 🤔👀 👩🏫💍
creep
@@bloxshortsdaily971
How sway
SteveLovesGOD creep
You guys don't like jokes huh?
Where were u when I needed u in school....love her
Who have tomorrow a test 🥺
Ooof thank you! I was having a hard time understanding this topic but your way of explaining it is awesome! RIght now Im taking college pre calc but I was suprised to see that I watched this video back in High School for Algebra 2!
anyone know her PH acc?
Gotta love it when you find Aubrey Plaza's doppelganger teaching trig on the internet. Well done.
this woman is a savior
I like how you talk to us like 3rd graders. It makes everything really easy to comprehend.
Hello from Germany thanks for this wonderful explination my teacher will never be able to explain stuff like you do not even in 100 years
OMG U'RE A LIFE SAVER THANK YOUU
thank u so much for making this video! im rlly confused when it comes to sin, cos, and tan (specifically as to which one i should be using depending on the question) and u helped me so much! subscribed!
Your explanations are exceptionally clear, thank you so much for these videos!