Arduino Tutorial 36: Understanding How to Use Tilt Switches in Your Projects

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  • Опубліковано 15 січ 2025

КОМЕНТАРІ • 1,8 тис.

  • @brankostrbac5931
    @brankostrbac5931 10 місяців тому +14

    I am electrical engineer, this is the best tutorials I have ever seen!

  • @billlaird7332
    @billlaird7332 Рік тому +6

    GABRIELLA! I'm watching all of your Arduino tutorial videos in order and always to the end. I don't do every assignment, but when learning a new important point, I do the assignment to reinforce the learning. You are a Master Teacher and your teaching style is the best I have ever experienced. I have completely understood every lesson. I especially like the in depth explanations of the combination of software, hardware, and physics. Well done, sir.

  • @Chris_Bro_aka_MR_PLAT1NEM
    @Chris_Bro_aka_MR_PLAT1NEM 4 роки тому +47

    GABRIELLA! I'm currently on day 3 of going through these tutorials and I have done them all the way through including the homework in between. This stuff works!

    • @FEDERICO-tc3wn
      @FEDERICO-tc3wn 2 роки тому +2

      Gabriella!

    • @dema3619
      @dema3619 2 роки тому +5

      you are incredible fast! congratulations, you are a really fast

  • @emiliomartineziii2980
    @emiliomartineziii2980 2 роки тому +3

    At the start of the video I paused and built the entire thing and got it to work by myself!

  • @MajdMazin
    @MajdMazin 4 роки тому +10

    Gabriella. I have been watching till the end every single one since the beginning. You have been a godsend good sir. I highly appreciate all the effort you put into these tutorials, it is not lost on us. You are a truly exceptional teacher and a delight to watch and learn from.

  • @hbar2028
    @hbar2028 2 роки тому

    Gabriella.
    Been watching all your videos beginning to end at work on my breaks. Then when I have time at home, I redo them again step by step. Great videos sir! Learning so much.

  • @terrymiller1600
    @terrymiller1600 3 роки тому +13

    Paul, I also am an Engineer but, I went to school in the age of vacuum tubes. I was the RTU Engineer at my local electric utility. Your videos are very professional informative. I do watch every lesson to the end. I also spent 7 years in the Ivory Coast as a Peace Corps volunteer. Thanks for the wonderful classes. I do really appreciate the insight. BTW, Happy Birthday and enjoy your time with Gabrella.

  • @Zpheme12
    @Zpheme12 5 місяців тому +1

    you are one of the greatest you tubers for electronics education. (Gabriela)

  • @johnmills353
    @johnmills353 4 роки тому +6

    Hi Paul,
    Gabriella !!
    Following your whole series of newer Arduino tutorials, just finished No 36 (tilt Switch).
    I always watch them to the end, I have about a 50% success rate with the assignments.
    You have got the mix of practical and theory just about right in my opinion.

  • @sumantakumardutta986
    @sumantakumardutta986 Рік тому +1

    Done the assignment by myself after pausing the video. Got it right in the first shot itself. Really had fun!!!😃😃😄

  • @tonygolden8622
    @tonygolden8622 3 роки тому +4

    Hello again Paul. Now that I have completed the project and watched the end of the lecture it is time to mention Gabriella. I have watched all of your videos, some more than once.
    I have completed all the projects, got many of them right, made mistakes on others, but learned something and had fun with all of them.
    I see that you have many other courses, enough to keep me busy for a long time. It is hard to imagine all the work it took to produce them.
    I really like the spontaneous feel, like one is working along with you at the same time, and your sense of humor is spectacular. Now on to lesson 38, 39, …….
    Tony

  • @satisfactoyz
    @satisfactoyz 3 роки тому +1

    Today's homework was much easier to complete without instruction. And it was your birthday! Lucky man to have such a beautiful grand-daughter! Thanks for another great lesson.

  • @kaindradjoemena7789
    @kaindradjoemena7789 4 роки тому +4

    Awwww Gabriella looks cute
    Happy birthday Paul!
    I just made a robot the other day that follows light. Nope, I did not copy anyone’s code. I did it myself. Thank you

  • @Rorschachcollision
    @Rorschachcollision Рік тому +1

    I am a programmer and engineer, so have very little patience for these things - but the wife had to point out that you and I are both Scorpios. So happy birthday, great teacher, and know that I will follow your tutorials always to the end, with coffee in hand.

  • @cmartin6126
    @cmartin6126 2 роки тому +3

    Hey Mr.Paul! Another glorious video tutorial. I am very grateful for the hard work that you put into these amazing tutorials. Keep up the good work! Gabriella looks excited!
    -STILL not Carole, just her son.

  • @aaronmilliman7685
    @aaronmilliman7685 2 роки тому

    Seeing the children healthy and Happy is the best birthday gift ever! Happy Birthday and Gabriella looks so happy.

  • @ayratkutlushin5252
    @ayratkutlushin5252 5 років тому +128

    String birthday = "Happy Birthday!";
    String granddaughter = "Gabriella";
    void setup {
    serial.begin (9600);
    }
    void loop {
    if (11/12 = your birthday && granddaughter=coming home) {
    serial.print(birthday);
    serial.print("clue word");
    serial.println(granddaughter);
    }

    • @AhmedMohammed-kz6ej
      @AhmedMohammed-kz6ej 4 роки тому +4

      hahahah this is so cute

    • @Vivalavidapool
      @Vivalavidapool 4 роки тому +1

      haha, I second that!
      Great video!

    • @ac8228
      @ac8228 4 роки тому +17

      That's wrong, it should be == because it's conditional

  • @eswarelectronics4205
    @eswarelectronics4205 3 місяці тому +1

    The video js 4 years old but delighted happy birthday ❤❤❤

  • @delroybarnes2041
    @delroybarnes2041 4 роки тому +24

    Made it to the end ans saw "Gabriella"; see much more than 3 minutes worth.

  • @Jobbe59
    @Jobbe59 11 місяців тому

    Gabriella! I watch all your lessons to the end. Don't want to miss a second of them.

  • @musicalhamsa5892
    @musicalhamsa5892 4 роки тому +4

    the 3 dislikes are the people who dont like coding

  • @bilbo593
    @bilbo593 9 місяців тому

    I am a retired Electronic Repair and did my course back the 70's with AWA Corp and Industrial Electronics . I am enjoying keeping my mind active and re learning things. I closed down my Repair Business back in 2008 and since then I have lost touched with everything electronics and all the latest innovations. Gabriella was happy to catch the plane to come and see you. And a very Happy Birthday!!

  • @dannycollins5698
    @dannycollins5698 Рік тому

    This was fun. I taught this to my 4 boys and wife. It was fun letting them hold the tilt switch. I asked them what they felt. It was fun to see them enjoy learning. 4, 6, 8, and 10 are the ages of my boys. This is so wonderful to take the code and to the physical world. It is fun thinking about what projects we can do with all that you have taught me. My boys have ideas of what we can do together. Look forward to paying it forward to my boys and may a school someday!
    We started with an experiment from the Feynman Physics lectures/exercises this morning and then did this.
    Wow -- how blessed I am to study Physics with Feynman and Computer Science with you Mr. McWhorter!!!

    • @paulmcwhorter
      @paulmcwhorter  Рік тому

      Great that you are making this investment in your boys. Well done!

  • @_ZN13
    @_ZN13 Місяць тому

    GABRIELLA! Took me some time to understand the story but since tutorial 34, I've been doing the homework on my own, and the happiness, when it's correct, basically kills me! 2024 and still the best Paul. Hats off man, you're amazing!

  • @tonygolden8622
    @tonygolden8622 3 роки тому

    Hi Paul. I’m just another old dog trying to learn some new tricks. You are a great teacher. Thanks for your generosity of spirit.

  • @amiamso
    @amiamso Рік тому

    GABRIELLA, I just want to say THANK YOU for all your videos. Yes, I watch them to the end, and then go back and pice-meal them into the code project i'm working on. Oh... and no, I don't do my homework. I take a coffe break with you. Thanks again for all that you do.

  • @عبدالرحمنالعيدروس-ض1ت
    @عبدالرحمنالعيدروس-ض1ت 3 місяці тому +1

    GABRIELLA! really thank u, I did the assignment and every thing, again thanks a million.

  • @JohnyRalte
    @JohnyRalte 3 роки тому

    Gabriellaaaa!!! Not only did I watch all your videos from start to end, I have watched some videos twice. You are a good teacher.

  • @digitaldoubter
    @digitaldoubter 10 місяців тому

    Gabriella!! I'm a computer science student who has a passion for building things with my hands, your tutorials have been awesome and I'm really thankful for this series!

  • @eddiedunseath9063
    @eddiedunseath9063 Рік тому

    I also used else instead of 2 if's on this. I jump back into your lessons to check things as I'm doing my homework (sometimes for only a few minutes, as you say), because I started your most excellent tutorials only 2 months ago, following my 80th birthday Arduino gift, and my brain velocity is much lower than it was 60 years ago! Also in this project i stuck my tilt switch to my stepper motor cardboard arrow (motor fixed vertically), connected using a pair of female/male wires. It switches the red/green LED's, but also controls the stepper motor direction, clock/anticlockwise, like a wiper blade. Thanks for your really excellent lessons Mr Paul. I used to live in Addis Ababa, love Africa and its wonderful people! Hi Gabriella !!

  • @MrBrentc74
    @MrBrentc74 3 роки тому

    Gabriella looks like a bundle of joy! I saw the mistake as you were typing it. Still need to wrap my head around the toggle switch logic, but was able to do the homework just fine. Thanks for the effort you give in sharing this knowledge. We are truly blessed to be able to learn this because of beautiful people like yourself!

  • @muhammadrafiqulislamkhan6994
    @muhammadrafiqulislamkhan6994 2 роки тому

    Happy Birthday. God bless Gavrialla. I do not know how many times I watch your video to understand your project. Every time a new thing comes out to me. Your debugging process is wonderful. It helps students where they are made mistake. Today I learn why I put TiltVal in place of TiltPin into serial.println because we already have tiltPin=2. I know it easy for everyone to undetstand but it is really difficult in past to me but today my legendary teacher Paul all clear to me. Thanks for everything Paul. God bless you.

  • @dubrocadidier4583
    @dubrocadidier4583 2 роки тому

    GAVRIELLA ....
    This Homework was cleared fast
    😀 thanks Paul. I have been watching all your videos to the end. Most times I replay as many times as possible to understand the concepts. Especially the ''PUSH BUTTON AS TOGGLE'' lesson.😄

  • @Anmol-AK
    @Anmol-AK Рік тому +1

    Gabriella!!
    Sir your content is great, thanks a lot for making these videos.

  • @zachhamersley967
    @zachhamersley967 3 роки тому

    Don't understand why people wouldn't finish the videos, but I like to understand how things work. Make it to the end every time, I thought that was the point. Did the homework on my own the same way you did, I think I'm starting to get this stuff. "Gabriella". Thanks for the videos Paul!

  • @israelkolawole7144
    @israelkolawole7144 2 роки тому

    Hi Gabriella, Mr. Paul has taught me a lot and am very grateful so give him lots more applause

  • @timothyflanagan7775
    @timothyflanagan7775 2 роки тому

    All the info you put into your videos; does NOT go to waste with this student

  • @daniel-yd7bq
    @daniel-yd7bq Рік тому

    Gabriella! You are the best teacher I have ever had, I'm glad you made this series

  • @victorlove3558
    @victorlove3558 3 роки тому

    Gabriella, I am very appreciative of your easy to follow and understand lessons. I'm in my seventies and doing Arduino for the first time.

  • @rodchristen2705
    @rodchristen2705 Рік тому

    I watched to the end and did my own coding!! Thanks for your help. I hope you had a great time with Gabriella as she was coming to see you. Grandkids are great!!!!!

  • @ve5wil
    @ve5wil Рік тому

    ive been enjoying your tutorials. they are among the most comprehensive ive seen on UA-cam. ive been able to complete most of a pet project with your series.

  • @johnryall5711
    @johnryall5711 3 роки тому

    Many Happy Returns Paul, made it to the end AND made it work! Granddaughters are precious, enjoy your time with Gabriella.

  • @mystreteacher
    @mystreteacher 2 роки тому

    Gabriella. Thanks for putting this series together. I'm an Assistive Technologist for students with disabilities and I'm just starting down the Auduino path so I can make more customized and sensitive switches for the students I work with.

  • @bersrk_burgr
    @bersrk_burgr Рік тому

    Gabriella! Was able to do the homework on my own. Just proof of how awesome of a teacher you are! Keep it up Paul!!

  • @gilnasty82
    @gilnasty82 2 роки тому

    GABRIELLA is precious!! Truly a gift from God!! :-) I can't believe average view time of your videos is only 3 minutes!! WOW!! I find myself anxious for more!! Can't wait to start the next lesson! HAPPY BIRTHDAY PAUL!! (late by a few years sorry)

  • @kirstinlee6838
    @kirstinlee6838 11 місяців тому

    Happy birthday! Your granddaughter Gabriella is adorable! I was so excited to do the homework by myself. Thank you so much for these videos.

  • @noobcoderandmaker
    @noobcoderandmaker Рік тому

    I'm watching Paul!. Enjoying the series so far. I also made it to the end, as I have with all your videos.

  • @Sam-rz5hw
    @Sam-rz5hw 3 роки тому +2

    And i am watching this lecture on my birthday!!

  • @ironsaberacademy
    @ironsaberacademy 3 роки тому

    Thanks!

    • @ironsaberacademy
      @ironsaberacademy 3 роки тому

      happy belated birthday paul have a cup of coffee on me :P gabriella looks so excited to come and see you i definately watch them all the way through i managed the homework by myself this time super proud of that :)

    • @paulmcwhorter
      @paulmcwhorter  3 роки тому

      WOW! Thanks . . . that is such an encouragement to me.

  • @abdulfx5030
    @abdulfx5030 5 місяців тому

    GABRIELLA! Thank you engineer. I have an electronics engineering degree. Thank you for giving this free tutorial. It was one of the best tutorials I've watched.

  • @SimulatedDigitalReality
    @SimulatedDigitalReality 16 днів тому

    Gabriella! Happy late birthday! Celebrating the New Years and enjoying myself with your tutorials! :D

  • @davidkeynton3402
    @davidkeynton3402 3 роки тому

    Yes, I got to the end and completed the homework before watching how you did it. Am enjoying all your videos. Gabrielle.

  • @panzerblitz8226
    @panzerblitz8226 2 роки тому

    Thanks Paul, your tutorials are the right length, and you explain so well!! I did the HW, and it worked perfect because your prior lessons are very clear and building on previous stuff that has a nice flow to it. You have a beautiful grand-daughter Gabriella. God Bless you and your family.

  • @diessos
    @diessos 2 роки тому

    Gabriella..... took a few months off due to other commitments. But was able to easily do this on my own. Really like these videos. I am finally understanding how all this works.

  • @alecgriffiths790
    @alecgriffiths790 Рік тому +1

    Gabriella! And yes, I was able to figure out how to set up and program the LEDs with the tilt switch without having to simply copy what you were doing... for once, haha! Hopefully that means I'm finally figuring this stuff out. This was a great tutorial, and I'm looking forward to watching the next one.

  • @angusclarke8592
    @angusclarke8592 2 роки тому

    Thanks, Paul. My Maths is actually non-existent so I'm very slow at working these things out. But trying a new thing in my late 60's gives me a new challenge in life. Welcome to Africa. I see you've now re-located. Very Brave at your age, but obviously Higher Hands are leading you. And Gabriella is a sweetie. So Cute.

  • @CK-sv8fc
    @CK-sv8fc 3 роки тому

    Happy Birthday Paul!! --Gabriella--
    As soon as I heard "pause this video" I immediately went ahead and did the homework.

  • @benthompson6118
    @benthompson6118 Рік тому

    Gabriella. I recommend all of your video tutorials to anyone who asks me where to learn arduino, pi, fusion360, or python.

  • @ABAT58
    @ABAT58 3 роки тому

    Thank you very much, Paul. That is because you are printing the pin not the value you just read. Thank you for your trick. You are a wonderful instructor.

  • @Aliguibrisa393
    @Aliguibrisa393 Рік тому

    Gabriela
    I watch your videos all times to the end thank you for your time

  • @BarryWilcockson
    @BarryWilcockson Рік тому

    Gabriella. I watch all tutorials to the end. They are so informative and easy to understand. Happy birthday.

  • @Mr_Jonathan_Greer
    @Mr_Jonathan_Greer 5 місяців тому

    I really like the homework. It forces me to recall things that I have learned and figure it out on my own. I really enjoy the way you do these lessons! Great work!

  • @yigitpar6492
    @yigitpar6492 2 роки тому

    Gabriella! Not a single second is wasted by skipping it. I have very limited time during the day because of work+parenting, but I am here to learn, not to memorise some stuff for a day or two. Hoping one day I'll tell/show someone what I learned, so I gotta be prepared :) Thanks a lot

  • @agonslay9173
    @agonslay9173 Рік тому

    3 years late but Happy Birthday!!
    Also Gabriella looks like an angel.
    I thing you are the sweetest and coolest grandpa that everybody would want

  • @HASANALI-wd1yl
    @HASANALI-wd1yl 2 роки тому

    happy birthday Mr. McWhorter, you absolute legend!

  • @sapphirereaper1252
    @sapphirereaper1252 10 місяців тому

    Gabriella! and that's for every video so far. This series is absolutely brilliant!

  • @daveCotterill
    @daveCotterill 16 днів тому

    GABRIELLA! , I paused the video and got it work before watching the end. This was one of the easier one's, the toggle switches code I find harder!. Brilliant learning video's, thank you very much.

  • @yassin9749
    @yassin9749 3 роки тому

    I know i miss it on 2019 but ur 2021 birthday will be after 2 months so HAPPY BIRTHDAY!! Gabriella !! and have watched all ur tutorials from start to finish and i will keep watch till last one

  • @ve3tvb
    @ve3tvb 7 місяців тому +1

    Happy bday Paul and gaveralla

  • @jeffnixon8338
    @jeffnixon8338 6 місяців тому +1

    Gabriella. Love your explanation and coding, Paul. I’m Jeff from Australia

  • @ravishankarkumarparibrajak4754
    @ravishankarkumarparibrajak4754 5 місяців тому +1

    Happy Birthday sir❤❤❤🎉🎉🎉

  • @jabber2824
    @jabber2824 8 місяців тому

    Love this course! And yes did my homework and watch til the end. I bet Gabriella is having her own Arduino kit by now. Cheers!

  • @graemedurden8975
    @graemedurden8975 2 роки тому

    Lovely smile Gabriella! And happy birthday Paul!
    Excellent video Paul, thanks. My project, when I get there will need tilt switches.

  • @daniellehwing4667
    @daniellehwing4667 9 місяців тому

    Gramps Paul must be so proud!!

  • @PerStigberg
    @PerStigberg Рік тому

    "Gavriella".
    Off course I always follow your videos to the end. Well, I did my homework and I did it well after two mistakes ("Red" instead of 1, "Green" instead of 0). Always fun to follow your Lessons.

  • @benoitgmarcotte
    @benoitgmarcotte Рік тому

    Gabriella - I really like your videos Mr. McWhorter. Thank you very much, you're a great teacher!

  • @MechElec208
    @MechElec208 3 місяці тому

    Gavriella? I did the homework on my own. Thanks Paul. Another terrific lesson!

  • @frankbonsignore.RochesterNY

    Gabriella!!! And belated happy birthday!! Great tutorial Paul. Simple homework which I readily achieved. Thank you. You are the best!

  • @caltech-wirewizard
    @caltech-wirewizard 2 роки тому

    Gabriella !!
    Yes, I go from start-to-finish on each video in succession and I enjoy them! And YES, each and every assignment.

  • @philnewman1110
    @philnewman1110 Рік тому

    I always make it to the end even if I have the video two or three times (Your benefit Paul) and I worked out the fault that was in there before you showed it! Im so pleased with myself! GiddyUp Gabrielle!! Thanks Paul.

  • @arseivan
    @arseivan 2 роки тому

    Hey Paul, thank you for another lesson (Gavriella)! I did this one before watching you doing it. Below is the code I ended up having. Nice way to simplify the if statements here - since we read 0 and 1 already we can incorporate these values in the digitalWrite statements:
    int greenPin = 8;
    int redPin = 9;
    int tiltPin = 53;
    void setup() {
    pinMode(greenPin, OUTPUT);
    pinMode(redPin, OUTPUT);
    pinMode(tiltPin, INPUT_PULLUP);
    Serial.begin(9600);
    }
    void loop() {
    bool tiltVal = digitalRead(tiltPin);
    digitalWrite(redPin, tiltVal);
    digitalWrite(greenPin, !tiltVal);
    }

  • @josemurillo227
    @josemurillo227 Рік тому

    Gabriella!! I am 3 years and change in the future wishing you a very late happy birthday PAUL! haha. Also, I was able to do the homework on my own the only thing different I just put the else statement instead of another if statement. Great video once again !!

  • @tntragan
    @tntragan 2 роки тому

    Welcome Gavriella. Love the grandkids. I am doing every homework assignment and watching every video to the very end. I must admit that sometimes the assignments take me quite a while to figure out. This one was very simple though. Thanks again for the amazing way you are teaching. I have learned so much and I intend on watching every video of this series and plan to watch your other videos as well.

  • @agustinruiz2081
    @agustinruiz2081 2 роки тому

    Gabriela. I watched until the end. I was able to complete the assessment myself, I think it was easy as I had watched all your videos previously.

  • @jaydusterhoff2795
    @jaydusterhoff2795 2 роки тому

    Gavriella. Struggled with the homework for a bit until I realized I used the wrong brackets. Worked great after that lol. Happy very belated birthday Paul, hope you had a great day.

  • @utahasweseeit
    @utahasweseeit Рік тому

    I made it to the end and did the homework on my own. Gabriella. Grandchildren are the best.

  • @ExquisiteConscience
    @ExquisiteConscience 2 роки тому

    Gabriella, great video Paul I am very happy that I am going through these lessons. I am learning alot.

  • @RavensHammer00
    @RavensHammer00 Рік тому

    Gabriella! Got it by myself, thank you! Thinking of buying the kits for a nephew or two who might be interested in these videos, I know I love doing the lessons! Thanks for your time in doing these, I watch on my TV, but comment via the computer, that way I can keep my IDE area a little neater. Sorry to hear people watch for so short a time, they could learn so much if they took the time to do so!

  • @nathanjones455
    @nathanjones455 2 роки тому

    Gabriella. You're an excellent teacher. Thank You.

  • @patrickserlippens3515
    @patrickserlippens3515 2 роки тому

    great tutorials, I watched all 36 untill the end for now and will be following the rest also

  • @akm5611
    @akm5611 3 роки тому +1

    Hi Paul, I think your lessons are great. I have had some programming in C about 25 years ago and it seems to be like riding a bike, most of it came back. Thanks for the videos, having a great time with my Arduino.

  • @scrappybobbarker5224
    @scrappybobbarker5224 3 роки тому

    Gabriella! I have watched every previous arduino tutorial in this series as well.

  • @sujalnath1797
    @sujalnath1797 2 роки тому

    Gabriella, I have watched the complete tutorial sir. Really, learning a lot. Thank you Sir.

  • @terryhoward986
    @terryhoward986 3 роки тому

    Thanks Paul always watch to the end, no problem with homework, the difference was I used the else statement rather than second If statement. Looking forward to future lessons.

  • @Mrerrol13
    @Mrerrol13 3 роки тому

    Although today is May 21st , I imagine it is November 12th and...Happy Birthday, Paul! Hahahaha!
    Great! I did it! I got worried when I saw that it didn't work but it was because I forgot to put the double == sign... fixed it quickly!
    And thanks for the prize! Gabrielle's smile is worth it!!!

  • @banyincam
    @banyincam 8 місяців тому

    I showed my son the green on tilt red project and he was amazed. I explained that it was as simple as two connections and a little ball. I even unplugged it and rattled the ball inside. He then suggested a magnet and sure enough, the magnet doesn't even have to touch it. It simply gets close and the lights change color. Gabriella!

  • @hassanbo8200
    @hassanbo8200 3 роки тому

    (Gabriella)
    I watch till the end of the video cuz I really want to learn arduino, and your videos are actually funny so I automatically watch it till the end.
    Best Regards Teacher Paul.

  • @vincentgirard8045
    @vincentgirard8045 3 роки тому

    This wasn't the first time that I have attempted the homework but it was the first time that I successfully completed it without having to cheat. Thank you for all your work.

  • @parulchhabra2939
    @parulchhabra2939 3 роки тому

    Happy Birthday Mr Paul, seeing the video 2 years after you posted it and coincidentally on your birthday date 🙂. You are an excellent mentor so can't miss any part of the video and yes saw Gabriella !!!!

  • @brandonreeder7704
    @brandonreeder7704 3 роки тому

    Many happy belated birthdays Paul! Thank you for the great lessons!

    • @brandonreeder7704
      @brandonreeder7704 3 роки тому

      Also, I enjoy the mini lessons on the inner workings of the components. You're very right, someone has to know how to do the math!