unity – Getting array of points shaping curve from 2 vector3 points

What I want is to get path for DoTween method DoPath(), which as a parameter expects array of vectors shaping the direction of the path. I googled some stuff and found out nothing. Just think bezier curve is good idea but i dont even know how it works. Here is an ilustration of my problem
enter image description here

The movement must be curved, don’t need linear one.
Thanks in advance

ag.algebraic geometry – Why is this “the first elliptic curve in nature”?

The LMFDB describes the elliptic curve 11a3 (or 11.a3) as “The first elliptic curve in nature”. It has minimal Weierstraß equation
$$
y^2 + y = x^3 – x^2.
$$

My guess is that there is some problem in Diophantus’ Arithmetica, or perhaps some other ancient geometry problem, that is equivalent to finding a rational point on this curve. What might it be?

fitting – Any way to draw a curve by hand and use the data and fit a function on datas?

I’d like to draw a simple curve by hand.
Next, I have to figure out what function defines it the best.

I’ve been thinking long but I don’t have an idea how to make it.

What I could imagine is that somehow draw series of points with drawing tools and get coordinates and then fit an arbitrary function to the coordinates.

In a similar topic someone suggested to use Classify but I don’t understand how it helps here.

So I don’t know how to start, any idea?

real analysis – existence of a non-trivial zero curve

Look at the ring-shaped area $ mathcal {A}: = {(r, theta) in mathbb {R} ^ 2: 1 leq r leq 2 } $. Suppose that $ f: mathcal {A} rightarrow mathbb {R} $ is a smooth function satisfying $ f | _ {r = 1} <0 $ and $ f | _ {r = 2}> 0 $. Also assume that the zero amount of $ f $ is a collection of smooth curves. Is it true that there is a component of? $ {f = 0 } $ What winds around the origin?

comment: Continuity of $ f $ implies that on every curve that connects the outer boundary of $ mathcal {A} $ at its inner limit there is a zero of $ f $. However, only this observation does not imply the existence of a zero curve that winds around the origin.

Thank you so much!

Calculus – Calculation of the overestimation of the displacement for the speed curve v (t) = 10 + 5t-t ^ 2 (further information in the body)

I'm a little confused about how I do this question. Link to question here

The question specifies a speed-time function (v (t) = 10 + 5t-t ^ 2) and asks whether the shift should be determined with an overestimation U5 (determination of the overestimation with 5 rectangles). The confusing part, however, is that the question is that the speed is constant after every second interval. This confuses me because f (2) = 16 f (2.5) = 16.25 and f (3) = 16 and I don't know if I should use 16.25 for the overestimation.

Does the picture here exactly show what the overestimation would look like according to the question? or would touch the middle rectangle 16.25 f (2.5) as this is the largest number between the interval 2 and 3. The main co-fusion results from the wording of the question “You have to determine the displacement of the vehicle after 5 seconds by assuming that the speed of the vehicle is over constant
every one second time interval. & # 39;

Read the question carefully and tell me what you think the overrated U5 should be. For me it's either 76 units ^ 2 or 76.25 units ^ 2.

f (1) + f (2) + f (3) + f (3) + f (4) = 76
or
f (1) + f (2) + f (2.5) + f (3) + f (4) = 76.25

differential geometry – straight line curve in a surface (=> planar and geodetic) that is not a line of curvature

I try to create a curve with these requirements, but all straightforward Curve that I get is Line of curvature.

I guess I have to use the fact that the second derivative is 0 because it's straightforward, but I don't know why it takes me so long to find one.