Cambridge Mathematician Reacts to Animation vs Geometry
Summary
TLDRIn this video, Ellie, a Cambridge Mathematics graduate, reacts to Alan Becka's 'Animation vs. Geometry'. She dives into fundamental geometric concepts like points, lines, and angles, and explores advanced topics such as the golden ratio, Pythagorean theorem, and fractals. The video is a blend of educational content and engaging visuals, with Ellie's enthusiasm for mathematics shining through as she explains and reacts to the complex mathematical animations presented by Alan Becka.
Takeaways
- π Ellie, a Cambridge Mathematics graduate, is reacting to Alan Becka's 'Animation vs. Geometry' video.
- π Ellie has previously reacted to 'Animation vs. Mathematics' and 'Animation vs. Physics', both linked in the video description.
- π The video begins with basic geometry concepts, such as Euclid's postulates and the fundamental idea of two points connected by a line.
- π The character 'Orange' is introduced, who Ellie previously referred to as 'Stickman', highlighting Alan Becka's history in animations.
- π Concepts like angles, ratios, and the golden ratio are explored, with the golden ratio being represented visually with a flash of gold and the number 1.618.
- π Geometric shapes like triangles, parallelograms, and squares are discussed, with an emphasis on the properties of 90Β° angles and Pythagorean theorem.
- π’ Mathematical drama unfolds as a 4D object appears, causing conflict and leading to the use of geometry and the golden ratio to combat it.
- π₯ The video features a mix of dimensions, with 1D, 2D, and 3D objects being used to limit and eventually trap the aggressive 4D object.
- π The use of platonic solids, including the tetrahedron, octahedron, and cube, is highlighted as a means to contain the 4D object.
- π Fractals and their significance in the video are mentioned, with the destruction of the 4D object revealing beautiful fractal patterns.
- π¬ The video concludes with a connection back to 'Animation vs. Physics', suggesting a thematic link between Alan Becka's animations.
Q & A
Who is the host of the video reacting to Alan Becker's animation?
-The host of the video is Ellie, a Cambridge Mathematics graduate.
What is the main topic of the video?
-The main topic of the video is a reaction to 'Animation vs. Geometry' by Alan Becker.
What are the first two postulates of Euclidean geometry mentioned in the video?
-The first postulate is that two points can be connected by a straight line, and the second postulate is that any line can extend to an infinite length.
What is the significance of the orange character in the video?
-The orange character, previously referred to as 'Stickman', is a recurring element in Alan Becker's animations and represents a key character in the 'Animation vs.' series.
What mathematical concept is represented by the golden ratio in the video?
-The golden ratio, approximately 1.618, is a mathematical concept that appears in various forms of art, architecture, and nature, and is shown as a significant element in the video.
What is the Pythagorean Theorem and how is it depicted in the video?
-The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the video, it is visually represented with shapes and angles.
What is the significance of the fractal patterns shown when the 4D object destroys things in the video?
-The fractal patterns that appear when the 4D object destroys other objects may symbolize the self-similarity and complexity found in mathematical structures, even when broken down or 'destroyed'.
What are the platonic solids mentioned in the video and why are they significant?
-Platonic solids are three-dimensional geometric shapes with equal faces and angles. In the video, they are the tetrahedron, octahedron, and cube, which are significant as they represent the first three of the five possible shapes that can be made with all sides of equal length.
How does the video use the concept of dimensions to create a conflict?
-The video creates a conflict by having a 4D object interact with and attempt to destroy 1D, 2D, and 3D objects. The conflict escalates as the 4D object is limited and eventually trapped by the use of higher-dimensional shapes.
What is the significance of the continued fraction of the golden ratio shown in the video?
-The continued fraction of the golden ratio is a way to express the ratio in a repeating pattern that never ends. It is significant in the video as it is used as a tool by the orange character in the conflict with the 4D object.
What is the final outcome of the conflict between the 4D object and the geometric shapes in the video?
-The final outcome is that the 4D object is trapped within a 3D object, which causes it to explode and reveal fractal patterns, suggesting a resolution to the conflict through the use of higher-dimensional geometry.
Outlines
π Introduction to Reacting to Alan Becka's Animation vs. Geometry
Ellie, a Cambridge Mathematics graduate, introduces her reaction video to Alan Becka's 'Animation vs. Geometry'. She expresses excitement for the topic, having previously reacted to Becka's videos on animation versus mathematics and physics. Ellie's channel focuses on STEM content, and she dives into the video expecting a foundational geometry lesson, starting with the definition of a line and points in space, referencing Euclid's postulates. She also mentions the 'orange' character from Becka's animations, showing her growing familiarity with the series.
π Exploring Basic Geometry Concepts and the Golden Ratio
The video script discusses fundamental geometry concepts such as lines, angles, and ratios. It highlights the significance of the golden ratio, approximately 1.618, which is a fundamental aspect of geometry. Ellie speculates about the relationship between the golden ratio and other geometric figures like triangles and rectangles. The script also touches on the possibility of Pythagorean theorem being introduced and the idea of geometric figures like squares and circles. The golden ratio is personified as a character, 'F', who interacts with 'Orange', leading to a narrative within the geometry lesson.
π’ Delving into Advanced Geometry: Platonic Solids and Fractals
The script moves on to more complex geometric concepts, including the introduction of Platonic solids and fractals. It describes the appearance of a 4D object, possibly a tesseract, and its aggressive behavior towards 2D and 3D geometric figures. The narrative includes the use of the golden ratio as a weapon against the 4D object and the appearance of a fractal plane. Ellie attempts to explain the significance of the fractal patterns revealed when the 4D object destroys geometric creations, indicating a deeper layer of complexity in the video's narrative.
πΉ Geometry in Action: The Battle with 4D Objects and Fractals
The script describes a dynamic scene where geometric figures, including a golden kite and a golden spiral, are used to combat a 4D object. The battle involves various geometric solids, such as a tetrahedron, octahedron, and cube, which are used to trap and limit the 4D object's capabilities. Ellie speculates about the significance of the dimensions and the progression from 1D to 3D objects in the battle. The script also mentions the appearance of a dodecahedron, another Platonic solid, and the explosion of the 4D object, leading to a display of fractals.
π The Conclusion: Reflections on Alan Becka's Animation and Geometry
In the final paragraph, Ellie reflects on the video's content, expressing a desire for more after the conclusion of the animation. She comments on the fractal patterns and the appearance of a dragon fractal, as well as the infinite reflections seen in the video. Ellie also notes the connection to the film 'Inception' and the concept of infinite worlds, tying back to previous videos she has made. She ends with a sense of satisfaction from watching Alan Becka's animation and invites viewers to join her for the next video.
Mindmap
Keywords
π‘Geometry
π‘Euclid's Postulates
π‘Golden Ratio
π‘Right Angle
π‘Pythagorean Theorem
π‘Platonic Solids
π‘Fractals
π‘Golden Spiral
π‘Continued Fraction
π‘4D Object
π‘Animation vs. Geometry
Highlights
Ellie, a Cambridge Mathematics graduate, reacts to Alan Becka's 'Animation vs. Geometry' video.
Introduction to Euclid's postulates, starting with two points connected by a line.
Orange, previously known as Stickman, represents a character in the animation.
Exploration of geometry concepts like extending lines, opposing angles, and right angles.
Discussion on the golden ratio, denoted as 'phi' (Ο), and its significance in geometry.
Introduction of Pythagorean theorem with a visual representation of a^2 + b^2 = c^2.
Transformation of geometric shapes into a parallelogram and square, illustrating geometric relationships.
Concept of increasing the number of equal triangles around a point to form a circle.
Appearance of the golden triangle and its relation to the Golden Ratio.
Introduction of the golden square and its mathematical properties.
Incorporation of fractals and the concept of a 4D object, suggesting a tesseract.
Use of the golden ratio in a continued fraction format, showcasing mathematical representation.
Appearance of the golden spiral, another feature in mathematics related to the Golden Ratio.
Introduction of the golden kite, a polygon with golden ratio properties.
Engagement with platonic solids, including the tetrahedron, octahedron, and cube.
Struggle between the 4D object and the geometric figures, leading to a mix of dimensions.
Final entrapment of the 4D object using a dodecahedron, a 3D representation of the Golden Ratio.
Exploration of fractals and their patterns when the 4D object destroys geometric figures.
Inception-like scene with infinite reflections and the appearance of a dragon fractal.
Connection to the previous video 'Animation vs. Physics' with a subtle tie-back.
Transcripts
today I'm going to be reacting to Alan
Becka's animation versus geometry let's
dive straight into
[Music]
it hi everyone and welcome back to my
channel for those of you that knew her
my name is Ellie and I am a Cambridge
Mathematics graduate and I am reacting
to animation versus geometry today this
is the third Alan Becka video that I've
reacted to so I did the animation versus
mathematics and the animation versus
physics both of the videos I've Linked
In the description so if you're fancy
checking them out after this video then
feel free I am so excited for this I
wasn't expecting animation versus
geometry to be the next one out I know a
lot of people were speculating about
maybe chemistry so I'm very happy that
it has aligned with mathematics because
yeah I love maths as most of you that
have watched this channel before know
and that's why this channel is here
because all I do is nerd out about stem
stuff so yes without further Ado let's
dive straight into animation versus
geometry okay we've got Circle a nice
shap in Geometry is it a
circle oh it's a line okay okay so
straight away we've got uh two I guess
points in space that are connected by a
line two points that are connected by a
line is the very fundamental aspects in
Geometry which is ukids postulates and
this is the first one that we see so
well I hope it is anyway I did this in
the animation versus m and I was like oh
this is what it is and then it just
wasn't so maybe I should just stop
talking there's a l there's a little
orange is this like a Tracker oh my gosh
that's orange that is something as well
that I in the previous two videos I just
got used to calling the stickman
stickman because I wasn't fully aware of
Alan Becka's whole history behind
animation whereas I know it now so yeah
um thank you YouTube for teaching me
something so I now know that Stickman as
I called them is now orange or the
second coming so I'm going to stick with
orange just cuz it's a bit faster so I
assume this is
Orange is that his head yeah okay
cool okay so orang is on ID's first
postulate which is two points connected
in space please don't jump off okay he
didn't we got we've got gravity again
here I guess oh a okay nice A and B
typically in Geometry when we label
points um just yeah generally in
Geometry we label them capital A B C and
throughout the alphabet so a the first
two letters in the alphabet and so these
points are connected by
that okay I have a feeling because he's
sticking his leg out he's going to fall
off there at some
point okay we've got another point is
this going to be C once it's connected
oh is C nice but it's not okay C is not
connected but it extends I guess it's
not infinite but maybe this is alluding
to the is it the second postulate I
think of uet's five postulates which
basically says that any line can extend
an infinite length I assume that's what
the arrow is indicating here they kind
of it can go on for forever essentially
cool okay so are we going to like step
through each of UK's postulates this is
like starting geometry stuff I feel like
most of Alan Becka's things just jump
straight into like really complex maths
so I'm glad that we're yeah
we're at like a nice level okay so C is
oh nice are we are we going to turn
start talking about vectors maybe um you
know Direction lines with directions no
oh cool okay oh this is throwing me back
to like mat in school I love geometry so
much sorry anyway I'll stop nerding out
apologies for how much I pause and nerd
out in this video so we have opposing
angles they're equal essentially if you
have two lines that cross then the
opposite angles here are exactly the
same so we have 60Β° and 60Β° um because
the opposite maybe we get on to talking
about how angles add up to
360 hopefully Okay so we've got 30 30 10
10 90Β° okay nice a right angled a right
angle should I say a right angle in
mathematics is uh an angle that measures
90Β° or pi/ 2 so here we see a nice thing
in mathematics which is yeah 90Β° I'm
sure we're going to see Pythagoras at
some point I'm waiting for
it nice we see here that an an angle on
a straight line is 180Β° we see that 2 90
de angles make
180 so again we've got degrees angles on
a straight line adding up to 180 it's
nice got ratios cool so we have the
ratio there of this point so the point
itself that says a colon B that's the
ratio between A and B so we see here
that the ratio between A and B so
because B is longer than a we expect the
ratio between A and B to be yeah less
than one
okay he's kicking it like a football
whoa what the heck was
that I got an
advert I got an advert at the at the
time that I was trying to figure out
what this gold thing is oh hang on a
second I'm going to rewind
it I'm going to pause it I think it's
the gold is it the golden it's got to be
the golden ratio like this is like one
of the most fundamental things in
Geometry I'm going to be quiet cuz I
feel like whenever I suggest things it's
always wrong so I think it's the golden
ratio because it's
1.618 yeah and we're getting a flash of
gold
1.618 yes okay nice okay okay cool
what oh
it's oh my gosh I think I laughed a bit
too hard then oh my gosh my throat yes
we have we have have five which is
typically denoted as the golden ratio so
I'm anticipating if it's anything like
Alan Becka's videos these two are
probably going to be enemies now let's
see so a so is there a significance of
the fact that a the ratio between A and
B is root three there perhaps maybe
later he's going to
fall is this going to make like a square
is he going to
help the golden race sure going to
help oh he did help oh I was fully
anticipating the golden ratio to start
fighting him okay cool cool I guess
they're friends are they going to be
friends or are they going to be enemies
like always in Alan Becka's
videos so we've got a 90Β° triangle okay
have I missed anything no we've got a 90
degrees triangle I anticipate
maybe Pythagoras's Theorem is going to
come up now
no okay we've just got the two two
triangles that are the same they can be
put together to form a rectangle nice
that works for 90Β° angles who so much is
happening so we've extended we've
rotated the lower triangle by 90Β° so
we're seeing a bit of how things are
related oh and it's just been flipped
across the axis which could be the
x-axis okay so we parallelogram nice so
two two that's just I feel like I'm
giving like a a lesson about geometry
here I'm trying to do my best to explain
what's going on here while it's also
reacting so excuse the constant
explanations but we have a parallelogram
because we can get two 90Β° triangles uh
we can combine them and they can make a
parallelogram which is what we see here
and the same goes for a
square oh nice okay
so this is relating to the fact that if
you increase the number of equal
Triangles around a
point then they extend towards a
circle which I expect expect is what's
yeah this is what's happening nice so
nice he's now a hamster on a car
carousel we've got this we've got the
circle okay nice and wow I paused at a
really good time there I was just going
to say that we have the um typical
geometry which is you can have a a
square a square no not a square at all a
triangle inside a circle um if you have
three points connected on a circle it
makes a triangle there's actually a
really cool I think it's a pum problem
about this which yeah I won't I'm
digressing I'm just nering out so
this is the um the
golden my brain's broken CU is happening
but the Golden Triangle because here you
see that the hypotenuse of the triangle
has length of the Golden Ratio
1.618 nice so we've got a Golden
Triangle so much has already happened
and we're only three minutes in we're a
third of the way in
okay I expect nothing less of of Alan
Becka's animations and now we have a
golden
square is it the golden Square here's
Pythagoras here's Pythagoras I was I was
waiting I thought it would come a bit
earlier but yeah here's the the classic
Pythagoras's Theorem which says that a s
+ B2 = c^2 of a triangle where a B and C
are denoted here so this is the kind of
visual representation of Pythagoras's
Theorem I like the music the music is
nice it's kind of similar to the
animation versus
physics but it's calm now
and as with all of Alan Beckers there's
going to be some drama I just know it
and this music is going to is going to
change
so we've
got I I feel like that's the golden
ratio changed from having a circle it as
five as as to a square and I imagine
that's him saying can you lift up a squ
as well like I've just done with c squ
yeah
that's come on orange I really hope I
haven't called him Stickman I feel like
I've been defaulting so if I have I
apologize okay nice
nice we've got a 2 + b s = c^2 and
obviously we had it for f as
C uh
okay uh rewind um
what okay so the music's changed and
that hang on that
before that looks like a
fractal is it a
fractal hang
on this I imagine is the the thing we're
now going to have to destroy as in all
of the animation series but that I'm
sure that is that that's got to be a 4D
object
because I'm thinking of like a tesseract
and a tesseract has kind of the
connected points out and then
into the like cubis I'm not explaining
this very
well but I'm sure this is a 4D object
it's CAU a bit and I imagine maybe
that's why
it's well I don't think it's so friendly
it doesn't look friendly anyway so it's
wanting to destroy the creations of F
and
orange yeah wait that is a fractal I
think that's a fra it's a fractal plane
okay so the behind is a fractal plane
that's kind of cool I wonder what the
significance is of the fact that we have
this really
aggressive 4D object and when it
destroys things it reveals a fractal
element I wonder what the significance
is of that
but this is so cool okay I mean it's not
cool cuz the the probably well they
won't die we know they won't die
okay oh just so much happening okay
right so we've got this 4D object that's
trying to
kill orange not Stickman and F or the
golden ratio and we've got we've got
another line uh here that they're
running
along well there's no like multiplier
for him to use to go faster now
whoa oh that's so cool okay it's the
um what do you call it it's like the
it's a fraction it's a continued
fraction it's the continued fraction of
five so essentially you can rewrite the
golden ratio I wonder I wonder if I can
just fast forward a bit here without
it yeah it's hard to kind of see but
essentially this here is the continued
fraction of f itself so we can write by
In This format which was also a really
cool thing that I learned just when
learning about the golden ratio I think
it's so cool just in math I find it so
cool how you can take something that's
like as simple as a as like a number or
an equation and you can write it in such
sometimes really neat format and I love
that about the film The Man Who Knew
Infinity because you see like patterns
that seem so complex can be written in
like a really nice format um yeah if
you're interested actually I've done a
video explaining the ma behind the film
The Man Who Knew Infinity so yeah check
that out if you're interested but anyway
we've got the continued fraction here of
F and orange is using that as ammunition
nice okay I like how when it shoots you
can see the reflection of so essentially
it's shooting a line and then you see
you're seeing it reflected and when
that's reflected you're seeing the angle
at which it's it's reflected cool
this is pretty close I mean it's always
close oh
okay okay oh okay nice we've got the
spiral we have the golden spiral we have
the golden ratio spiral it's beautiful
another
beautiful um feature in mathematics I
would say and the 4D 40 objects coming
back
okay right so much has happened there
we've got the golden ratio being used as
a a balancing object and orange is I
assume going to shoot a line yeah
nice I mean back to the spiral itself I
just find again I'm going to n out there
are so many really cool features in
mathematics or so many called patterns
in maths and they can be seen in nature
as well which are yeah just find
fascinating okay so orang is being a
surfer or a skater Now using F okay Okay
so we've got a golden kite we have a
golden kite kite should I
say 4D object is shooting more 4D
objects I think why does this look like
Space Invaders this is
crazy the music is so intense as well oh
my
gosh
okay I'm not seeing any mathematics I'm
seeing mathematics
nice and we're seeing a pentagon and a
pentagon that's made up of different
golden ratios which is why it's golden
beautiful and now we've got loads of
little FS okay and they're creating
objects to destroy this 4D object which
is just getting even angrier okay oh
we're seeing fractal patterns again this
is so awesome I I really want to know
what the significance is
behind the the reason why when the 4D
object
ruins aspects of this hang on
there's like the mini little Tessa thing
that I was saying but it's not Tesseract
at all it's just like a cube with a
little circle inside it I assume they're
going to try and trap the 4D object in a
3D
object
okay so much violence I
mean
okay oh nice right right so he's the 4D
object is now trapped inside a
tetrahedron which is
a four-sided object I don't know why
that took me so long he's trapped inside
a tetesan okay which seems to have
worked and this is no longer tetrahedron
it is an octahedron I believe so he's
enclosed
in this three-dimensional space now
which seems to be entrapping here
and now he's going to be enclosed even
further
in a square is it a square yeah Square
oh nice okay we've got like three we've
got no we had we've got two solids there
platonic solids which uh essentially
mean that well I think that's right
platonic solids were are they equal
sides or at least they're
solid so much is happening but
essentially we just created three
different
three-dimensional objects which I think
are referring to the platonic solids
that is it platonic solids I hope it's
bonic solids which are
three-dimensional geometrical objects
which all their sides are equal so we
had the tetrahedron we had the
octahedron and then we had the cube
which are the first three out of the
five objects that can all be made by
having the same size lengths I I think
but then I said that about the
postulates and I said we'll see all the
postulates which we probably have I just
I probably missed all of them
um Okay so we've got a lot of golden
objects
here he's rotating the golden objects
okay are we going to get another
platonic solid here yes yeah wait wait
wait wait wait wait wait I forgotten
what it's called but I'm sure that is
one of the other platonic solids I'm
sure of it because we've got we've got
triangles there and they're all equal
length like well they are equal length
as well but equal all the triangles are
exactly the same in the solid itself so
I think we have the platonic solids okay
I I really hope I haven't messed that up
okay and it seems to be that these
platonic solids are stopping the 4D
object or at least limiting the 4D
objects
capabilities um we're mixing Dimensions
here which oh I kind of understand that
like the when you think about it I mean
I really hope that is a 4D object like I
said if it's not then this Theory fails
but obviously we saw two-dimensional
objects being you know straight lines
being shot at well not
actually wow my brains just clicked we
started with
one-dimensional objects being shot
at the 4D object which were just
straight lines we saw that didn't limit
him at all all this 4D object then we
started with two dimensional objects
being shot at the 4D object limited the
4D object a little bit further but not
massively and now we're on to
3D all right okay
cool uh I'm actually really quite proud
of myself for hopefully picking that up
so now 3D is limiting the 4D object even
further I anticipate maybe we will try
and trap the 4D object in a 4D object
itself Maybe I'm I'm thinking that's
where it's going let's have a
look okay
wow so we used this platonic solid to
ENT
trap now they're going to do they're
going to make it but with pentagons yeah
that's a do decahedron okay I know I
know that name I forgotten what the name
of the one that we had
previously I forgot on the name of the
object the 3D object we had previously
okay nice
nice wait did that just get did that
just explode hang on wait wait wait so
we we we've entrapped the do we've
entrapped that's actually really nice so
essentially all of the uh segments where
their points connect in the center of
this four-dimensional object we've
entrapped that into a three-dimensional
object which has caused it to blow
up it's like Stardust it's so cute
maybe not cute
but okay whoa oh we've got fractals
again oh we've got we've got the dragon
fractal is it Dragon fractal dragon tail
Dragon
something I absolutely love the effect
of the combination between like the the
negative whoa hang on let me just pause
and explain what I was going to say my
camera also just died at the worst
possible time but what I was saying was
back to the whole fractal thing I really
I really how we've got like this
negative 4D object and when it destroys
things in the 3D 2D 1D world we have
these fractal patterns and you know
fractals in Geometry I just find
fascinating in themselves if you want me
to do a video on them I'm more than
happy to because I can just nerd out all
day about them um and I've also paused
it on a what looks like incept is it
Inception is that the film where kind of
an infinite set of mirrors it's like
when you go to like an amusement park
and there's like other mirrors and you
don't actually know which way to get out
so we've got we still have the do
decahedron orange
is stood looking at
himself suppose this is fractal in
itself kind of an infinite number of
seeing him in infinite times whoa hang
on so we're
seeing I think they're they're are they
4D
objects so we're seeing loads of
different 4D objects I think
okay I knew there'd be some sort of tie
back to the previous video which is
animation versus physics and as I said
in that video This Ain't his first rodeo
so I like that little subtlety there
that's scary that's I mean that's kind
of like going back to like the infinite
worlds Theory which I've done a video on
literally my last video was on that but
how you can see yourself in a parallel
universe so we see orange
in a parallel universe with this Cowboy
hatan which is from animation versus
physics
crazy
okay that's
spooky
a oh I'm kind of sad that's over I like
I was kind of I don't know I was just
kind of wanting more um I feel like
that's me at the end of every single one
of Alan Becka's videos a good way to
spend a Saturday thank you to everyone
who's watched this video and I'll see
you all in the next one
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