Uploaded December 2025 | Updated September 2026, 3 weeks ago
In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative of the vector function that represents the curve. Although I recap on the derivation for the plane curve arc length I did in my previous videos, I do not go over the proof for the space curve length in this video; perhaps in a future video.
I also go over an example on determining the length of a section of a circular helix, as well as plotting it in GeoGebra's amazing 3D graphing calculator: geogebra.org/3d/gbvmtdug
#math #vectors #calculus #arclength #geogebra
Timestamps:
- Arc Length of a plane curve with parametric equations – 0:00
- Recap on Arc Length derivation from my earlier videos – 1:43
- Arc Length of a space curve is defined in the same way as for plane curves – 5:55
- Compact form of the arc length formulas as the integral of the length or magnitude of the derivative of the vector function – 9:28
- Recap on the distance formula in 3D (and 2D) – 13:08
- Example 1: Arc Length of a Circular Helix –14:11
- Arc length = 2(2^(1/2)pi ≈ 8.89 – 17:40
- Graph of the helix from Calculus Book and from GeoGebra – 19:27
Notes and playlists:
- Summary: inleo.io/threads/view/mes/re-leothreads-2lbgt2xzq
- Notes: peakd.com/@mes/koxharrd
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Gd5OieYiZMaSKw1QfyHbiG
- Vector Functions playlist: youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .
------------------------------------------------------
Become a MES Super Fan! youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: peakd.com/@mes
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative of the vector function that represents the curve. Although I recap on the derivation for the plane curve arc length I did in my previous videos, I do not go over the proof for the space curve length in this video; perhaps in a future video.
I also go over an example on determining the length of a section of a circular helix, as well as plotting it in GeoGebra's amazing 3D graphing calculator: geogebra.org/3d/gbvmtdug
#math #vectors #calculus #arclength #geogebra
Timestamps:
- Arc Length of a plane curve with parametric equations – 0:00
- Recap on Arc Length derivation from my earlier videos – 1:43
- Arc Length of a space curve is defined in the same way as for plane curves – 5:55
- Compact form of the arc length formulas as the integral of the length or magnitude of the derivative of the vector function – 9:28
- Recap on the distance formula in 3D (and 2D) – 13:08
- Example 1: Arc Length of a Circular Helix –14:11
- Arc length = 2(2^(1/2)pi ≈ 8.89 – 17:40
- Graph of the helix from Calculus Book and from GeoGebra – 19:27
Notes and playlists:
- Summary: inleo.io/threads/view/mes/re-leothreads-2lbgt2xzq
- Notes: peakd.com/@mes/koxharrd
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Gd5OieYiZMaSKw1QfyHbiG
- Vector Functions playlist: youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .
------------------------------------------------------
Become a MES Super Fan! youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: peakd.com/@mes
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
