How to Inscribe a Polygon inside a Circle || General Method

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

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  • @joshuadenanie3742
    @joshuadenanie3742 2 หลายเดือนก่อน +17

    My students will surely shed tears 😂

    • @DragoFun8695
      @DragoFun8695 2 หลายเดือนก่อน +1

      Hi sir I didn't shed any tears I did do it

    • @leibniz4455
      @leibniz4455 หลายเดือนก่อน +2

      As a student not from your university, will confirm that we are not shedding tears, but shedding waterfalls

  • @AkkepallyAishwarya
    @AkkepallyAishwarya 3 หลายเดือนก่อน +1

    U really hit my expectations

  • @NorainDeLionAngnie-ny1xw
    @NorainDeLionAngnie-ny1xw 4 หลายเดือนก่อน +1

    Thanks you so much sir

  • @jitghosh6692
    @jitghosh6692 6 หลายเดือนก่อน

    Thank you so much sir ❤

  • @nastyYT1
    @nastyYT1 10 หลายเดือนก่อน

    nice one ADTW Study

  • @Goofayball
    @Goofayball 7 หลายเดือนก่อน +7

    Why is it 2 that the external point connects to?

  • @challariharshitha5885
    @challariharshitha5885 4 หลายเดือนก่อน +1

    Can we draw 6 sided polygon with this method

    • @Mrx-rv1ru
      @Mrx-rv1ru 3 หลายเดือนก่อน

      Yup

  • @nineprod3541
    @nineprod3541 ปีที่แล้ว +3

    How do I make a regular pentagon of side 2.5 cm.??

  • @mjeffery
    @mjeffery ปีที่แล้ว +7

    NOT a general method.
    While this does correctly inscribe a triangle, square, or hexagon in a circle, it does not work for other regular polygons. It does produce remarkably close results for a pentagon (.065% angle error), heptagon (.17% error), and octagon (.42% error), but the error continues to grow as the sides increase. By the time it reaches a 25-gon, the error is large enough to not even fit 24 sides in the circle.
    It's fine if you want to draw an n-gon approximation with a small number of sides, but don't use this on a math test.

    • @laslaminas
      @laslaminas ปีที่แล้ว +1

      we use it all over spain, not as an exact methow but as aproximate method

    • @Goofayball
      @Goofayball 7 หลายเดือนก่อน +1

      So what’s the best method?

    • @mjeffery
      @mjeffery 7 หลายเดือนก่อน

      @@Goofayball To inscribe an exact regular n-gon in a circle with straight-edge and compass? It's not possible because most regular n-gons cannot be constructed with straight-edge and compass.
      What you can do is inscribe a regular p-gon into a circle where p is a Fermat prime (a prime of the form 1 + 2^{2^n}), take an inscribed m-gon and n-gon and inscribe an LCM(m,n)-gon, and double the sides of an inscribed n-gon to get an inscribed 2n-gon.
      Combining the above allows the construction of a k-gon when k = 2ⁿ·p₁·p₂·p₃..., where the pᵢ values are 0 or more distinct Fermat primes. No other n-gon can be constructed. Note that there are only 5 known Fermat primes (3, 5, 17, 257, and 65537).
      So it's possible to construct an 8-gon (octagon) and a 60-gon, since 8 = 2³ and 60 = 2²·3·5, but not a 7-gon (heptagon) or 9-gon (nonagon) because 7 is a non-Fermat odd prime and 9 = 3² is the result of multiplying two non-distinct Fermat primes (3 with itself).
      Doubling a regular polygon just involves bisecting a side or angle and intersecting it with the circumscribed circle.
      Inscribing an LCM(m,n)-gon involves inscribing an m- and n-gon in a circle with a common vertex, then finding a pair of the nearest non-common vertexes between the m- and n-gon and copying that around the circle.
      Inscribing a Fermat p-gon in a circle can be done by memorizing the known cases-it's unlikely you'll need anything beyond the triangle and pentagon in practice. I'm sure there is a marvelous method to construct any Fermat p-gon which this comment is too narrow to contain.

    • @peterjeffrey8126
      @peterjeffrey8126 27 วันที่ผ่านมา

      The first metho, this is method 2​@@Goofayball

  • @noralive1366
    @noralive1366 2 ปีที่แล้ว +2

    can you draw a 7 sided regular polygon with this method?

    • @ADTWstudy
      @ADTWstudy  2 ปีที่แล้ว +5

      Yes, divide the horizontal line into 7 parts and draw a vertical line passing through point 2 on the horizontal line...

    • @lanceraltria
      @lanceraltria ปีที่แล้ว

      @@ADTWstudy pffffffftttttttt

    • @radhabai2666
      @radhabai2666 ปีที่แล้ว

    • @wiilli4471
      @wiilli4471 ปีที่แล้ว

      @@lanceraltria No you cannot. It will be an approximation but it will be slightly off. Try it yourself.

    • @wiilli4471
      @wiilli4471 ปีที่แล้ว

      @@ADTWstudy No you cannot. it will be a close approximation but not correct

  • @gajjze
    @gajjze ปีที่แล้ว +1

    Can you please explain me the reason that how that first side you get as one fifth of the circumference?
    I cannot get it don't know which property is used here .. please tell...

    • @ADTWstudy
      @ADTWstudy  ปีที่แล้ว +1

      Dividing the diameter of a circle into five equal parts, as illustrated, results in a distance between point A and 2-dash that is approximately equivalent to the length of one side of a pentagon. This constructional approach is employed to approximate the general shape of a pentagon. For precise length calculations, the formula 2Rsin36(degree) can be utilized, where R represents the diameter of the outer circle.

  • @Donvaga
    @Donvaga 9 หลายเดือนก่อน

    Ok

  • @shbmd451
    @shbmd451 22 วันที่ผ่านมา

    bruh complicating it too much, cant you just divide 360 by number of edges for polygon and just draw in circle using those angles to define the points, finally connect them and get it over with?

  • @SamuelLouis-c6x
    @SamuelLouis-c6x ปีที่แล้ว

    I HATE YOU MAKING ME DOING SOMETHING WRONG WITH MY WORK