Twist (mathematics) | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Twist_(...)
00:01:10 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
increases imagination and understanding
improves your listening skills
improves your own spoken accent
learn while on the move
reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services...
Other Wikipedia audio articles at:
https://www.youtube.com/results?searc...
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7308194308718224
Voice name: en-AU-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
Socrates
SUMMARY
=======
In mathematics (differential geometry) twist is the rate of rotation of a smooth ribbon around the space curve
X
=
X
(
s
)
{\displaystyle X=X(s)}
, where
s
{\displaystyle s}
is the arc length of
X
{\displaystyle X}
and
U
=
U
(
s
)
{\displaystyle U=U(s)}
a unit vector perpendicular at each point to
X
{\displaystyle X}
. Since the ribbon
(
X
,
U
)
{\displaystyle (X,U)}
has edges
X
{\displaystyle X}
and
X
′
=
X
+
ε
U
{\displaystyle X'=X+\varepsilon U}
the twist (or total twist number)
T
w
{\displaystyle Tw}
measures the average winding of the curve
X
′
{\displaystyle X'}
around
and along the curve
X
{\displaystyle X}
. According to Love (1944) twist is defined by
T
w
=
1
2
π
∫
(
d
U
d
s
×
U
)
⋅
d
X
d
s
d
s
,
{\displaystyle Tw={\dfrac {1}{2\pi }}\int \left({\dfrac {dU}{ds}}\times U\right)\cdot {\dfrac {dX}{ds}}ds\;,}
where
d
X
/
d
s
{\displaystyle dX/ds}
is the unit tangent vector to
X
{\displaystyle X}
.
The total twist number
T
w
{\displaystyle Tw}
can be decomposed (Moffatt & Ricca 1992) into normalized total torsion
T
∈
[
0
,
1
)
{\displaystyle T\in [0,1)}
and intrinsic twist
N
∈
Z
{\displaystyle N\in \mathbb {Z} }
as
T
w
=
1
2
π
∫
τ
d
s
+
[
Θ
]
X
2
π
=
T
+
N
,
{\displaystyle Tw={\dfrac {1}{2\pi }}\int \tau \;ds+{\dfrac {\left[\Theta \right]_{X}}{2\pi }}=T+N\;,}
...
Смотрите видео Twist (mathematics) | Wikipedia audio article онлайн без регистрации, длительностью часов минут секунд в хорошем качестве. Это видео добавил пользователь wikipedia tts 07 Октябрь 2019, не забудьте поделиться им ссылкой с друзьями и знакомыми, на нашем сайте его посмотрели 47 раз и оно понравилось 0 людям.