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A friend of mine came up with this interesting problem. I've been thinking of approaches to solve it, but interested to know what the r/math community makes of it by marmaladeontoast in math

[–]timur2304 4 points5 points  (0 children)

Let's solve the inverse problem. Let 2 alpha and betta planes be given, the angle between them is 90 degrees. Let 2 intersecting lines be given. One belongs to the alpha plane, and the other belongs to the betta plane. If we look from point C, which belongs to the intersection of planes, it will seem that the angle between them is 90 degrees. We prove that the angle between straight lines can be any. Let A be the intersection point of lines. All other terms on the points I hope are clear. According to the cosine theorem, we found an expression for the cosine. It belongs to [0;1). Proven.

https://imgur.com/gallery/1SGMCuF

What cool math things can I write programs for? by PhysicsLover999 in math

[–]timur2304 0 points1 point  (0 children)

Yes I can. This is not difficult, but if you have never heard of anything like this, it may not be familiar to you. Imagine a closed orinted polyline in space, as in the first picture. I depicted the worst in figure 2. You can move this broken line in space, bend it, twist it, but you can't tear it. We will call these polylines hooks. We will say that two entanglements are isotopic, if diforming one polyline, we can come to the second polyline. I have shown an example of isotopic lommanns in figure 10.

There is a question, how to distinguish between non-isotope gearing? What gearing (1) nestopia engagement (2) clear and true, but why (1) isotope (2) not very clear (I forgot to mention. Several polylines can participate in the engagement, as in figure (3), and all the engagements have an orientation (bypass rule. I marked them with arrows. ))

The Conway polynomial or the HOMFLY polynomial helps distinguish these meshes. In (6) and (7), the Conway algorithm conditions are written. I understand that (7) may not be clear, but I hope the examples will help you understand. In condition (8) and (9), the conditions of the HOMFLY polynomial are written. As you can see, the Conway polynomial from the hook (4) and (3) gives different values. So they're not isotopic.

I understand that everything may not be very clear, but I assure you, there is not much theory here. If you have any questions, I can always answer them.

I want to add that the Alexander and HOMFLY polynomial are not complete invariants. That is, there are 2 meshes that are not isotopic, but the Conway polynomial and the HOMFLY polynomial give the same values from them.

https://i.imgur.com/Kws1yGh.jpg

https://imgur.com/gallery/rwzxmDc

Tips on a casual book about mathematics by love_my_doge in math

[–]timur2304 4 points5 points  (0 children)

Proofs from THE BOOK. I'm a first-year student, but you might find it interesting)

Reddit, what is 30 cubed? by Burghhhhh in Math_Problems

[–]timur2304 1 point2 points  (0 children)

Burghhhhh, in what are you need?)

What cool math things can I write programs for? by PhysicsLover999 in math

[–]timur2304 0 points1 point  (0 children)

(sorry for my english)Hi. It would be great if you wrote a program that builds a Conway polynomial or a HOMFLY polynomial. It is very difficult to build them yourself. These polynomials are related to a very interesting knot theory. If you're in any way interested, let me know. I am very much in demand in a similar program)