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topology - 16.3k posts

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  • "To be more realistic, in order to construct a Cantor Set, we begin from a distance of one meter length and we subtract the central one-third (keeping the extreme points of the central one-third). In that way, two shorter spaces are left, with one-third of meter length: we subtract of these their central one-thirds. We repeat the process unlimited taking shorter and shorter spaces so we get to the limit where the construction has been repeated infinite times. This is the Cantor Set.
·
You will probably think that absolutely nothing remained. No, for example the points 1/3 and 2/3 dogded the subtraction, as the points 1/9, 2/9, 7/9 and 8/9. In other words, the extreme points of all the subtracted parts have remained. And as it can be proven, many other points have remained too.
·
The total length of the subtracted parts is 1, as much is the primary length of the space we began with. Therefore, in a way, the "length" of the Cantor Set is zero! This seems logic, the Set of Cantor is mainly constituted of holes - it seems more like dust than space.
·
Ian Stewart. Does the God play Dice? (The new mathematics of Chaos).
Basil Blackwell (1989).
°
°
°#mathsbeauty  #maths #math #mathematician #mathematicus #mathsinlove #mathsinlife #mathsforlove #mathsforlife #mathinlife #mathinlove #mathinworld #beautyinmaths #online #studying #theorem #exercise #cheat  #exercises #notes #notebook #book #mathbook #cantor #set #cantorset #topology
  • "To be more realistic, in order to construct a Cantor Set, we begin from a distance of one meter length and we subtract the central one-third (keeping the extreme points of the central one-third). In that way, two shorter spaces are left, with one-third of meter length: we subtract of these their central one-thirds. We repeat the process unlimited taking shorter and shorter spaces so we get to the limit where the construction has been repeated infinite times. This is the Cantor Set.
    ·
    You will probably think that absolutely nothing remained. No, for example the points 1/3 and 2/3 dogded the subtraction, as the points 1/9, 2/9, 7/9 and 8/9. In other words, the extreme points of all the subtracted parts have remained. And as it can be proven, many other points have remained too.
    ·
    The total length of the subtracted parts is 1, as much is the primary length of the space we began with. Therefore, in a way, the "length" of the Cantor Set is zero! This seems logic, the Set of Cantor is mainly constituted of holes - it seems more like dust than space.
    ·
    Ian Stewart. Does the God play Dice? (The new mathematics of Chaos).
    Basil Blackwell (1989).
    °
    °
    ° #mathsbeauty #maths #math #mathematician #mathematicus #mathsinlove #mathsinlife #mathsforlove #mathsforlife #mathinlife #mathinlove #mathinworld #beautyinmaths #online #studying #theorem #exercise #cheat #exercises #notes #notebook #book #mathbook #cantor #set #cantorset #topology
  • 1,199 3 29 December, 2018
  • What will I become? 
Surprised to find one more iso-area (almost same from both sides) tessellation out there. Watch it being born 🌊🌊🌊
  • What will I become?
    Surprised to find one more iso-area (almost same from both sides) tessellation out there. Watch it being born 🌊🌊🌊
  • 795 49 8 July, 2018

Latest Instagram Posts

  • Нашла крутые уроки по ригу лица, которые начинаются с правильной топологии. В свободное время буду потихоньку пилить 💫

#3dmaya #3dmodel #3dmodeling #3dface #topology #koskalapkoy
  • Нашла крутые уроки по ригу лица, которые начинаются с правильной топологии. В свободное время буду потихоньку пилить 💫

    #3dmaya #3dmodel #3dmodeling #3dface #topology #koskalapkoy
  • 6 1 3 hours ago
  • #KnotTheory {Slide 1/10)
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Mathematical studies of #knots began in the 19th century with #Gauss, who defined the linking integral In the 1860s, Lord Kelvin's theory that #atoms were knots in the #ether led to Peter Guthrie Tait's creation of the first knot tables Tabulation motivated the early knot theorists, but knot theory eventually became part of the emerging subject of #topology.
ㅤ
In the last several decades of the 20th century, scientists became interested in studying physical knots in order to understand knotting phenomena in #DNA and other polymers. Knot theory can be used to determine if a #molecule is chiral or not.
ㅤ
Besides, another area for the application of knot theory is statistical mechanics.
ㅤ
This application was left undiscovered until very recently. Vaughan Jones discovered the connection when computing a new polynomal in variant for knots. In this field, knots can used to represent systems and thereby increase the ease of the study.
ㅤ
Archaeologists have discovered that knot tying dates back to prehistoric times.
ㅤ
Besides their uses such as recording information and tying objects together, knots have interested humans for their aesthetics and #spiritual #symbolism.

#Lissajous #Knot #Torus #VortexGeometry369 #GeometriaVortex #GeometriaSagrada #Fractal
  • #KnotTheory {Slide 1/10)

    Mathematical studies of #knots began in the 19th century with #Gauss , who defined the linking integral In the 1860s, Lord Kelvin's theory that #atoms were knots in the #ether led to Peter Guthrie Tait's creation of the first knot tables Tabulation motivated the early knot theorists, but knot theory eventually became part of the emerging subject of #topology .

    In the last several decades of the 20th century, scientists became interested in studying physical knots in order to understand knotting phenomena in #DNA and other polymers. Knot theory can be used to determine if a  #molecule is chiral or not.

    Besides, another area for the application of knot theory is statistical mechanics.

    This application was left undiscovered until very recently. Vaughan Jones discovered the connection when computing a new polynomal in variant for knots. In this field, knots can used to represent systems and thereby increase the ease of the study.

    Archaeologists have discovered that knot tying dates back to prehistoric times.

    Besides their uses such as recording information and tying objects together, knots have interested humans for their aesthetics and #spiritual #symbolism .

    #Lissajous #Knot #Torus #VortexGeometry369 #GeometriaVortex #GeometriaSagrada #Fractal
  • 433 9 10 hours ago
  • The Acoustic Mirrors
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An engineered spatial acoustic experience: Stop by the Hexagon (HPH) in Hönggerberg for the opening of the acoustic mirrors! Tuesday 9th April, 9pm
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Prof. Dr. Klaus Ensslin (NCCR QSIT), Prof. Dr. Benjamin Dillenburger (NCCR DFAB), Marirena Kladeftira @marirena_kl , Maria Pachi @maria__pachi , Mathias Bernhard, Demetris Shammas @dshmms , Regina Moser, Dr. David Müller
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Photography: Marirena Kladeftira @marirena_kl
  • The Acoustic Mirrors
    -
    An engineered spatial acoustic experience: Stop by the Hexagon (HPH) in Hönggerberg for the opening of the acoustic mirrors! Tuesday 9th April, 9pm
    -
    Prof. Dr. Klaus Ensslin (NCCR QSIT), Prof. Dr. Benjamin Dillenburger (NCCR DFAB), Marirena Kladeftira @marirena_kl , Maria Pachi @maria__pachi , Mathias Bernhard, Demetris Shammas @dshmms , Regina Moser, Dr. David Müller
    -
    Photography: Marirena Kladeftira @marirena_kl
  • 154 5 18 hours ago
  • Smileberry のTopology-connecting music-ツアー大阪に参戦してきました😊
ちょっと遅れての参加で、もったいなかったですが、初めてスマベリのワンマンに行けて嬉しかったです😊
相変わらず、律さんはえらいカッコいいし、フリはたくさん間違えたけど、楽しかった〜🤣もときさんはやっぱり歌上手い!もっと聴きたかったなぁ💦
撮影会、行きたかったけど勇気が出なかったです😢
スマベリのライブ、また行きたいです!
#smileberry 
#Topology-connecting music-
#スマベリ 
#osakaruido
  • Smileberry のTopology-connecting music-ツアー大阪に参戦してきました😊
    ちょっと遅れての参加で、もったいなかったですが、初めてスマベリのワンマンに行けて嬉しかったです😊
    相変わらず、律さんはえらいカッコいいし、フリはたくさん間違えたけど、楽しかった〜🤣もときさんはやっぱり歌上手い!もっと聴きたかったなぁ💦
    撮影会、行きたかったけど勇気が出なかったです😢
    スマベリのライブ、また行きたいです!
    #smileberry
    #Topology -connecting music-
    #スマベリ
    #osakaruido
  • 5 0 21 March, 2019
  • поверхность боя
сегодня я побалую вас такой вот штуковиной.  как видно, это очень простая форма, которая приведет в восторг архитектурных критиков. я откопал ее в книжке по топологии, в которой среди серьезных формул частенько встречаются такие вещи как "шутовской колпак", или "яйцо дунса". именно здесь кружка и бублик - одно и то же, сферу можно вывернуть наизнанку, а Перельман получает и отказывается от миллиона. а еще они любят стрелочки (не так сильно, как Грэм, конечно).
#топология #математика #рисунок #поверхность #topology #maths #drawing #handgraphics #surface #handdrawing #mloa
  • поверхность боя
    сегодня я побалую вас такой вот штуковиной. как видно, это очень простая форма, которая приведет в восторг архитектурных критиков. я откопал ее в книжке по топологии, в которой среди серьезных формул частенько встречаются такие вещи как "шутовской колпак", или "яйцо дунса". именно здесь кружка и бублик - одно и то же, сферу можно вывернуть наизнанку, а Перельман получает и отказывается от миллиона. а еще они любят стрелочки (не так сильно, как Грэм, конечно).
    #топология #математика #рисунок #поверхность #topology #maths #drawing #handgraphics #surface #handdrawing #mloa
  • 13 0 21 March, 2019
  • CARA MENGGUNAKAN WATERPASS

Waterpass adalah alat ukur tanah yang berfungsi untuk mengukur ketinggian antara 2 titik atau lebih, biasanya Waterpass digunakan seseorang untuk menentukan beda tinggi di suatu tempat.
• Syarat pemakaian alat Waterpass :
-Syarat Dinamis : Sumbu I Vertikal
-Syarat Statis :
1. Garis bidik teropong sejajar dengan garis arah nivo.
2. Garis arah nivo tegak lurus sumbu I.
3. Garis mendatar diafragma tegak lurus sumbu I
4. Siapkan alat – alat yang di perlukan seperti : Alat ukur Waterpass, Bak ukur dan Tripod.
5. Letakkan Waterpass di atas Tripod.
6. Pastikan posisi garis mendatar diafragma yang terdapat pada waterpass sejajar dengan sumbu I.
7. Aturlah sekrup A, B dan C supaya gelembung nivo berada di tengah.
8. Tarulah Bak Ukur di suatu tempat yang ingin di ukur elevasinya.
9. Arahkan Waterpass ke arah objek.
10. Aturlah tombol focus / Mikrometer agar  objek yang di bidik terlihat jelas.
11. Setelah itu lakukan pengukuran dengan benar.
Sumber : https://muhammadalif461.wordpress.com/2016/12/14/cara-menggunakan-waterpass/
.
.
PT Dinar Energi Utama
Geoinstruments & Geotechnical Service
Business Inquiry : marketing@dinarproject.com
Website : www.dinarproject.com
.
.
#waterpass #echosounder #geophysical #gelogical #geologi #drilling #geodetic #pertambangan #dinarproject #geotechnicalservices #service #anakteknik #tekniksipi #topology #surveyortambang #surveyorindonesia #surveytambang #dradloading #echolaoading #kelautan #oceanography
  • CARA MENGGUNAKAN WATERPASS

    Waterpass adalah alat ukur tanah yang berfungsi untuk mengukur ketinggian antara 2 titik atau lebih, biasanya Waterpass digunakan seseorang untuk menentukan beda tinggi di suatu tempat.
    • Syarat pemakaian alat Waterpass :
    -Syarat Dinamis : Sumbu I Vertikal
    -Syarat Statis :
    1. Garis bidik teropong sejajar dengan garis arah nivo.
    2. Garis arah nivo tegak lurus sumbu I.
    3. Garis mendatar diafragma tegak lurus sumbu I
    4. Siapkan alat – alat yang di perlukan seperti : Alat ukur Waterpass, Bak ukur dan Tripod.
    5. Letakkan Waterpass di atas Tripod.
    6. Pastikan posisi garis mendatar diafragma yang terdapat pada waterpass sejajar dengan sumbu I.
    7. Aturlah sekrup A, B dan C supaya gelembung nivo berada di tengah.
    8. Tarulah Bak Ukur di suatu tempat yang ingin di ukur elevasinya.
    9. Arahkan Waterpass ke arah objek.
    10. Aturlah tombol focus / Mikrometer agar objek yang di bidik terlihat jelas.
    11. Setelah itu lakukan pengukuran dengan benar.
    Sumber : https://muhammadalif461.wordpress.com/2016/12/14/cara-menggunakan-waterpass/
    .
    .
    PT Dinar Energi Utama
    Geoinstruments & Geotechnical Service
    Business Inquiry : marketing@dinarproject.com
    Website : www.dinarproject.com
    .
    .
    #waterpass #echosounder #geophysical #gelogical #geologi #drilling #geodetic #pertambangan #dinarproject #geotechnicalservices #service #anakteknik #tekniksipi #topology #surveyortambang #surveyorindonesia #surveytambang #dradloading #echolaoading #kelautan #oceanography
  • 305 7 21 March, 2019
  • TAMBANG PASIR LUMAJANG DIBUKA LAGI

Aktivitas pertambangan pasir di Kabupaten Lumajang sudah dibuka kembali. Namun, Polres Lumajang akan segera memberlakukan pembatasan jam operasional armada angkutan material tambang yang membawa bahan tambang itu keluar dari Lumajang. 
Hal ini, masih katanya, telah dilakukan evaluasi dan kajian lapangan pasca penutupan tambang pasir, yang ternyata jalanan jadi teratur dan tidak terjadi antrian padat armada truk pasir. Meski, masih ada armada angkutanlainnya, baik angkutan kayu maupun tebu yang juga beroperasi di jalan dengan pelanggaran batas tonase.
Sementara itu AKP Rian Septya Kurniawan Kasatlantas Polres Lumajang menyatakan, bahwa sebelum keputusan pem batasan jam operasional truk di jalur Lumajang ini ditetapkan oleh Bupati dalam bentuk Perbup (Peraturan Bupati), maka pihaknya rutin melakukan upaya penertiban tonase muatan
Sumber : https://www.suarasurabaya.net/jaringradio/news/2016/181230-Sungai-Meluap,-Puluhan-Rumah-di-Lumajang-Tergenang-Banjir
.
.
PT Dinar Energi Utama
Geoinstruments & Geotechnical Service
Business Inquiry : marketing@dinarproject.com
Website : www.dinarproject.com
.
.
#pertambangan #migas #geophysical #gelogical #geologi #geodetic #pertambangan #dinarproject #geotechnicalservices #service #anakteknik #tekniksipil #topology #surveyortambang #surveyorindonesia #surveytambang #satelit #mapping #freeport #ESDM
  • TAMBANG PASIR LUMAJANG DIBUKA LAGI

    Aktivitas pertambangan pasir di Kabupaten Lumajang sudah dibuka kembali. Namun, Polres Lumajang akan segera memberlakukan pembatasan jam operasional armada angkutan material tambang yang membawa bahan tambang itu keluar dari Lumajang.
    Hal ini, masih katanya, telah dilakukan evaluasi dan kajian lapangan pasca penutupan tambang pasir, yang ternyata jalanan jadi teratur dan tidak terjadi antrian padat armada truk pasir. Meski, masih ada armada angkutanlainnya, baik angkutan kayu maupun tebu yang juga beroperasi di jalan dengan pelanggaran batas tonase.
    Sementara itu AKP Rian Septya Kurniawan Kasatlantas Polres Lumajang menyatakan, bahwa sebelum keputusan pem batasan jam operasional truk di jalur Lumajang ini ditetapkan oleh Bupati dalam bentuk Perbup (Peraturan Bupati), maka pihaknya rutin melakukan upaya penertiban tonase muatan
    Sumber : https://www.suarasurabaya.net/jaringradio/news/2016/181230-Sungai-Meluap,-Puluhan-Rumah-di-Lumajang-Tergenang-Banjir
    .
    .
    PT Dinar Energi Utama
    Geoinstruments & Geotechnical Service
    Business Inquiry : marketing@dinarproject.com
    Website : www.dinarproject.com
    .
    .
    #pertambangan #migas #geophysical #gelogical #geologi #geodetic #pertambangan #dinarproject #geotechnicalservices #service #anakteknik #tekniksipil #topology #surveyortambang #surveyorindonesia #surveytambang #satelit #mapping #freeport #ESDM
  • 107 1 21 March, 2019