geometry – Helix around Helix around Circle

I’m trying to find the parametric equations for a helix around a helix around a circle (helix on helix on circle)
That is: I would like to start with a circle, add a helix around it and a helix around the helix.(See video)

I’m ok even if the second helix is not perfectly orthogonal to the first helix as long as we can have a simpler parametrization.
I’m ok also if the curve represents a helix around a helix around a helix.

I know the helix around a helix around and an axis is quite easy but I was not able to find a solutions for this case.
I’m interested in this parametric curve as a way to represent time and I would like to write a program to show data attached to that curve.

error – Magento Checkout page goes hangs and infinite loop circle revolves after Paypal Payment fails

When customers is doing transaction on our website and going for payment to paypal and enters all details related to payment.

The user lands on checkout page on our magento website and circle spins continuously and transaction fails without any error message
Current Magento Version - 2.3.1

Error in logs 
main.critical: paypal nvp gateway errors: the field shipping address postal code is required.

Error in Paypal logs attached.

Please help us on this.

conic sections – From a point perpendicular tangents are drawn on the ellipse $x^2+2y^2=2$. The chord of contact touches a circle concentric with ellipse…

From a point perpendicular tangents are drawn on the ellipse $x^2+2y^2=2$. The chord of contact touches a circle concentric with ellipse. Find ratio of min and max area of circle

Let the point from which tangents are drawn be $(h,k)$

Then the locus of that point will be

Also the chord of contact is
$$frac{hx}{2}+ky-(frac {h^2}{2}+k^2)=0$$

Let the circle be $$x^2+y^2=a^2$$

Then the tangent to this circle is
$$y=frac{-h}{2k}xpm asqrt{1+frac{h^2}{4k^2}}$$

$$hx+2ky mp asqrt{4k^2+h^2}=0$$
Now I could equate the $c$ term of the linear equations, but that’s a very lengthy process, so I am convinced I am approaching the question wrong. How should I do it right?

dnd 5e – Circle of the Moon Druid discrepancy on dndbeyond

The article is correct, becuse of the modifications the Moon druid subclass does to the Wild Shape feature

Specifically, Moon Druids get the Circle Forms feature which explicitly overrides the CR restrictions of the normal Wild Shape (emphasis added):

Starting at 2nd level, you can use your Wild Shape to transform into a beast with a challenge rating as high as 1 (you ignore the Max. CR column of the Beast Shapes table, but must abide by the other limitations there).
    Starting at 6th level, you can transform into a beast with a challenge rating as high as your druid level divided by 3, rounded down.

Player’s Handbook, p. 69

This is an example of Specific Beats General, a principle outlined on page 7 of the Player’s Handbook (which is also in the Basic Rules) and reiterated on page 5 of Xanathar’s Guide to Everything.

strange circle always on the same area when aperture greater than 11

I have the same issue with Lens Model : 40mm when the aperture is greater than 11,
so im blocked for the long exposure too , it’s a known issue ? and how to fix it ??

Camera Model Name    Canon EOS 2000D        
Lens Model  Canon EF-S18-55mm f/3.5-5.6 IS II       
Shutter Speed    1/160  
Aperture     13.0   
ISO      100    
Focal Length     18.0 mm        
Focus Mode   One-shot AF    
Canon Firmware Version   Firmware Version 1.0.0 

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Geometry – The legs of a right triangle with a given hypotenuse and radius of the label circle

triangle $ Triangle ABC $ is a right triangle with $ measured angle ACB = 90 ^ circ $. To let $ AB = c $ and the radius of the labeling circle is $ r $. Find the cathets and the area of ​​the triangle $ Triangle ABC $.

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To let $ P, N $ and $ M $ be the tangent points with $ AB, BC $ and $ CA $, respectively. The square $ MINC $ is a square. That's why, $ MI = IN = NC = CM = r. $ We have $ AM = AP = c_1 $ and $ BN = BP = c_2 $ as tangential segments. Now we have: $$ begin {cases} (c_1 + r) ^ 2 + (c_2 + r) ^ 2 = (c_1 + c_2) ^ 2 \ c_1 + c_2 = c right arrow c_2 = c-c_1 end {cases}. $$ After simplifying the first equation, I got $ r ^ 2 + c_1r + c_2r = c_1c_2 $ and now let's get stuck $ c_2 = c-c_1 $. We get the quadratic equation $ c_1 ^ 2-cc_1 + r ^ 2 + cr = 0 $ that has roots $ c_1 = dfrac {c pm sqrt {c ^ 2-4r ^ 2-4cr}} {2} $. I'm not sure I understand what to do next and why we got two expressions for the same segment. What does that mean? Use both results in when using $ c_2 = c-c_1 = dfrac {c pm sqrt {c ^ 2-4r ^ 2-4cr}} {2} $. Which does ______________ mean?

Highest possible DC for Circle of Death

What is the highest possible DC for Circle of Death?


  • Level 12 Assistant (You can choose an archetype if it has a familiar one)
  • Cyphergull familiar
  • At least 3 unused general talent slots and one bonus talent slot (if the archetype removes bonus talent slots, 4 general talent slots must remain open.)
  • Only Pathfinder 1e content, Pathfinder content written in 3.5 (Elves of Golarion, Curse of the Crimson Throne, etc.) is not permitted.
  • Making magic items is allowed, but for a level 12 character, you're limited to a total of 1.5 WBL.
  • Custom magic items are not allowed. You are limited to printed magical items only.
  • Aside from spells with permanent / instant duration, you may consider 1 Round buffs. You cannot debuff the spell's targets.
  • Available spells (from items, magic services, etc.) are limited to spells that only level 12 or lower wizards can cast.
    • Ex. Fortune tellers receive an ether trip as a level 6 spell and can cast it at level 12 so that it is available. Wish cannot be cast from any level 12 and is therefore not available.
    • Ally / Army over time, Simulacrum, Planar Binding and Planar Ally are not available.
  • Items that impose a penalty, such as B. "Empty Shard" improve the DC of the spell so much. Example: Void Shard counts as an increase in Circle Death's DC by 2.

machine learning – VC dimension of the archery class on a unit circle

The input space is a unit circle. $ mathcal {X} = mathbb {S} ^ 1 subset mathbb {R} ^ 2 $. There is class $ mathcal {F} $ of arches on $ mathbb {S} ^ 1 $, where a point is labeled 1 if it is on the arc and 0 otherwise. We want to find the VC dimension of $ mathcal {F} $

I think the answer is 2. Any two points can be destroyed $ (++, – +, + -, -) $. But if we have three points $ {(x_1, y_1), dots, (x_3, y_3) } $ that all have the designation 1 with radius $ r_1 = r_2 = 1 $, and $ r_3 = 0 $It is impossible to smash them. Is my intuition correct?

Equation for a great circle with two spherical coordinates?

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Unit – How to place 3D text in a circle

For a project, I have to display a 3D button with surrounding text. At the moment it works perfectly, but I would like to place a round text instead of a straight text (similar to a cylinder skin).

Is it possible to achieve this effect with Unity Canvas? or how can I create a 3D button with a circular text encircling it?

Thanks for your help!!!

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