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Holditch's Theorem
License: CC0 1.0 Universal (CC0 1.0) Public Domain Dedication. creativecommons.org/publicdomain/zero/1.0
To the extent possible under law, I have waived all copyright and related or neighboring rights to this video. This work is published from: Brazil.
References:
[1] Holditch, H. (1858). Geometrical theorem. _The Quarterly Journal of Pure and Applied Mathematics_ , _2_ , 38. resolver.sub.uni-goettingen.de/purl?PPN600494829_0002
[2] Wetzel, J. E. (2010). An ancient elliptic locus. _The American Mathematical Monthly_ , _117_ (2), 161-167. doi.org/10.4169/000298910X476068
[3] Monterde, J., & Rochera, D. (2017). Holditch's Ellipse Unveiled. _The American Mathematical Monthly_ , _124_ (5), 403-421. doi.org/10.4169/amer.math.monthly.124.5.403
[4] Rochera, D. (2019). _On Holditch's theorem and related kinematics_ [Doctoral dissertation, Universitat de València]. roderic.uv.es/handle/10550/72339
00:00 Holditch's Theorem for Circles
00:50 Holditch's Theorem for Rectangles
01:11 Ellipsograph or Trammel of Archimedes
01:44 van Schooten's Locus Problem
02:01 Monterde & Rochera's Proof
05:04 Standard Proof
07:00 Non-Convex Examples
09:26 References
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КОМЕНТАРІ

  • @piotrbagnicki7162
    @piotrbagnicki7162 2 місяці тому

    It's EPIC! So much emotions, perfect singers, wow!

  • @shortsrapha
    @shortsrapha 3 місяці тому

    Cheguei

  • @thatrandomchannel8589
    @thatrandomchannel8589 4 місяці тому

    This video states exactly why I feel the way I do about laws.

  • @diode86
    @diode86 6 місяців тому

    17 years ago? Damn..this is depressing..

  • @lincolnuland5443
    @lincolnuland5443 7 місяців тому

    Amazing.

  • @overlord6455
    @overlord6455 7 місяців тому

    This is an interesting interpretation for 4D Tetris. I made a version of my own for my AP CSP create task titled "Tesseris," and it's quite different from this. Through my development, I tried to stick to the spirit of Tetris so as to expand the dimensions without adding new rules or mechanics. In my version, the board's dimensions are 6x6x6x10. The pieces fall through the 4th dimension, with the clearing method being to fill cubes. I chose this as I saw the evolution through dimensions being to fill lines (2D), rectangles (3D), and, ultimately, rectangular prisms (4D). However, I do like that the clearing method shown in this video plays on having to look at multiple different prisms at once, since it requires the player to really focus on the 4th dimension and be wary of mistakes across the whole board. The goal in my game is to fill 5 cubes, inspired by the 40 line sprint gamemode popular in modern Tetris titles today. My reasoning for having pieces fall through the 4th dimension was solely based upon the fact that pieces fell through the 2nd dimension in normal, 2-dimensional Tetris. Therefore, I chose the last dimension. I also felt that it presented a much greater strategic challenge having to stack on the 4th dimension. My version also followed closely by modern Tetris mechanics, including a hold piece and the 7-bag system. However, I did not use the Super Rotation System. I felt that SRS was too complex to easily translate into 4 dimensions, and I wasn't planning on being too ambitious when exam results were on the line. I kept the original 7 tetrominoes as the pieces for the game, which may sound easy to work with, but I made sure to add a tradeoff: rotation was very limited. To keep mirror pieces (e.g. S and Z) from being redundant, I made them rotate in different patterns. The system for rotation I stuck with was also simple and required very little code, which was a huge plus considering the complexity of 4-dimensional rotation. I can't tell, but I may be using the same rotation system as shown here. At the very least, rotating line pieces in my game behaves the exact same as the one that was rotated in this video. The limited rotation I chose made playing 3-dimensionally difficult, and, to be honest, I never figured out a plausible strategy to play 4-dimensionally. I'm sure there's one out there, though. I also visualized the board a little differently, though I did consider using the one shown here. Instead of showing all cubes at once, 2 inputs are added to shift between viewing each cube. Because the player could only see one cube at a time, along with the fact that the pieces fell through the 4th dimension, I opted to completely remove gravity, although pieces could still not be moved back "up" once lowered through the 4th dimension, and pieces that were placed would still go "down" until they hit something. I felt that having gravity added too much difficulty and held players back from strategizing. So, comparing this older interpretation of 4D Tetris to mine, I find it quite interesting that it still follows the same trend that normal Tetris games went through, putting more emphasis on game strategy (openings, efficiency, etc.) and less on survival skills as time progressed.

  • @micheleledonne9200
    @micheleledonne9200 9 місяців тому

    I love you from Rome Italy

  • @figgles2472
    @figgles2472 11 місяців тому

    Amazing animations ngl tho I need a voiceover cos my maths is not quite good enough to just look and see this and understand

  • @wingssj
    @wingssj Рік тому

    🔥🔥🔥🔥🔥

  • @OutragedPufferfish
    @OutragedPufferfish Рік тому

    Funny.

  • @KirbyBolha
    @KirbyBolha Рік тому

    Para Cada Lágrima Que Cai Encalhado em uma praia escura As ondas me trazem tristeza e com esta visão do passado na minha mente Tudo que eu mais quero é te ver voltar a viver Eu chamo seu nome Mas você não me escuta Eu procuro seus olhos mas eles não me veêm E quando eu tento alcançar suas mãos Percebo que não posso mais senti-las Eu vejo seus olhos Eu sinto sua dor No caminho das águas, eu me sinto à deriva. O vento me traz tristeza E uma visão do passado na minha mente Tudo que eu queria era não ter visto você morrer... Eu chamo seu nome Você não me escuta procuro seus olhos mas ele não me veêm E estou queimando por dentro, Espero que você esteja aí Não vê minhas lagrimas? Eu te vejo chorar! E eu tentei esquecer Você estará sempre nos meus pensamentos Eu olho nos olhos de um homem solitário Um homem que eu cuidava um homem que eu conhecia Pra cada lágrima que cai A ferida aumenta Na minha alma que já está sangrando... Se eu estivesse lá Oh deus, queria ter salvo você Ainda lembro os momentos que dividimos Tentei esconder a tristeza que sentia, Não acredito que fui levado pra bem longe Como se nunca tivesse existido Como se não tivesse feito parte da sua vida [Solo: Englund] Continuo encalhado em uma praia escura E a mesma onda me traz a tristeza E eu me sinto à deriva, sim, a deriva E minha ferida aumenta Para cada lágrima que cai Para cada lágrima que cai

  • @lourier3
    @lourier3 Рік тому

    I need a modern remake of this. I wanna play it!

  • @mrpepper666
    @mrpepper666 Рік тому

    Cade o Daniel Fraga

    • @wood-eye
      @wood-eye Рік тому

      Ele está vivo e bem.

  • @amits4744
    @amits4744 Рік тому

    Blockout (3D Tetris) is a good game and that should be extended to 4th dimension

  • @edenbeamie
    @edenbeamie Рік тому

    My father past away this February and every time I hear this song I just break , still it helps healing me. Thank you guys and in June I will see you live for the first time at Graspop with my little 12 year old daughter. No doubt I will be crying to this song but smiling at the end.

  • @RodrigoMarcheEncinas
    @RodrigoMarcheEncinas Рік тому

    Ótimo.

  • @kattis69
    @kattis69 2 роки тому

    Fina Carina💞

  • @caprise-music6722
    @caprise-music6722 2 роки тому

    Holy smokes! Can’t believe I’m commenting on a FIFTEEN year old UA-cam video!!

  • @rushfan5563
    @rushfan5563 3 роки тому

    This band is so freaking good

  • @yamadojo81
    @yamadojo81 3 роки тому

    This rendition of the song is simply beautiful, Tom's and Carina vocals are outstanding. Each time i listen to it i can't do nothing but be moved.

  • @emmap9466
    @emmap9466 3 роки тому

    my flex is that my dad's in there

  • @Carol0571
    @Carol0571 3 роки тому

    Beautiful x

  • @mikejacobs1149
    @mikejacobs1149 3 роки тому

    wow his wife has an amazing voice

  • @d.r.aderagingaction1302
    @d.r.aderagingaction1302 3 роки тому

    Is youtube algorithm alright? This is on my recommended and it's 10 YEARS ago... Oh this is an interesting game

  • @FallenYggdrasil
    @FallenYggdrasil 4 роки тому

    I'm still stranded on a shore of no light myself in 2020...

  • @БорисЕгоров-ш7ь
    @БорисЕгоров-ш7ь 4 роки тому

    Awesome!!!

  • @newgameld2512
    @newgameld2512 4 роки тому

    This was in 1990?!

  • @blewers
    @blewers 4 роки тому

    Totally totally amazing

  • @tadhg1959
    @tadhg1959 4 роки тому

    There are many songs by EVERGREY that I love, but this one here, may be my favorite. The deliverance of emotion is exceptional.

  • @roomofmadnesssweden6324
    @roomofmadnesssweden6324 5 років тому

    Sooo beautiful voices💚I love it!!

  • @DJRaptorXS
    @DJRaptorXS 5 років тому

    A mighty fine ballad from my fave band!

  • @ozzlayer
    @ozzlayer 5 років тому

    Powerful song and performance. I discovered this band by accident in 2003, then they released this live DVD in 2004. I bought the DVD and CD of this live performance. Soooo good.

  • @jarilindroos8831
    @jarilindroos8831 5 років тому

    Hope they last forever. If not. I'm sorry...yes i am...

  • @darrylburmeister1676
    @darrylburmeister1676 5 років тому

    Long live the beauty of EVERGREY

  • @jeannestecyszyn
    @jeannestecyszyn 5 років тому

    Man and wife, so beautifull, with fire in their hearts!!💚💚💚💚

  • @luiza1130
    @luiza1130 5 років тому

    Brasil 2019... amo essa música desde 2007😍😎

  • @petereerdekens7046
    @petereerdekens7046 5 років тому

    Majestic

  • @fallenangellangennutenkeli
    @fallenangellangennutenkeli 5 років тому

    Awesome song, full with soul and heart!

  • @Jamal-zn8sc
    @Jamal-zn8sc 5 років тому

    So romantic... :/ Adele was invited?

  • @amirpf
    @amirpf 6 років тому

    Carina Englund's voice is awesome!

  • @Dannybythebanana
    @Dannybythebanana 6 років тому

    Imagine a DT cannon

  • @zacharythomas5839
    @zacharythomas5839 6 років тому

    This song gives me tears. Tom looks like Oliver Platt. His wife is very pretty. This is first good look I have seen of her. She has an amazing voice too.

  • @ignatenko.a
    @ignatenko.a 6 років тому

    Такие молодые)

  • @mundus4732
    @mundus4732 6 років тому

    ♥️♥️♥️

  • @brianasciak1668
    @brianasciak1668 6 років тому

    one of the few DVD i yearly watch, and this one just make me shivers down my spine

  • @calebhein8043
    @calebhein8043 6 років тому

    This is such an amazing visualization of four dimensions! Why did I not think of this!?!?!?!?

    • @hannah42069
      @hannah42069 5 років тому

      It doesn't work with non-grid things and anything using a much bigger axis

  • @RolandsSteampunkery
    @RolandsSteampunkery 7 років тому

    So It's 4 games of 3D Tetris going at once, and the block's could be in any of those four games at once. Any MLG Tetris players out there??

    • @calebhein8043
      @calebhein8043 6 років тому

      It's not exactly four games of 3D Tetris, it's the effect of a tesseract passing through each of the planes, which we couldn't really access. Think about it all in one less dimension, otherwise, it gets more confusing. If we wanted 3D Tetris but we were a 2D being, we would have our normal Tetris game, but with five different things since we must fit them all into one 2D plane. Similarly, ... Nevermind. Take a higher dimensions class and inquire about Tetris in higher dimensions.

  • @exedeath
    @exedeath 7 років тому

    This game is strange, sometimes the piece have 4 cubes, other time it has 12 cubes, sometimes two. Also the board is 13x4x4x4, it should have been 20x10x10x10

  • @silviuchiparatu8804
    @silviuchiparatu8804 7 років тому

    True, evergrey congratulations,

  • @nutjohansson5377
    @nutjohansson5377 8 років тому

    varför inte på sweden rock hon har en röst som en gudagåva till er musik