Help to share beauty of math with more people

[fooz]

Hey everyone,

I’m working on an app (Math Journey) designed for those of us who appreciate beauty of mathematics. Unlike existing applications, it will dive into a bit more advanced topics (like the Riemann Zeta function and so on) but will maintain level of popular mathematics.
I’m looking for your suggestions on:

• Which advanced topics are rarely covered in typical apps but deserve more attention?
• Specific features you’d find exciting (e.g., interactive widgets, puzzle-based explorations, real-world case studies, etc.)?
• Any learning approaches that you’ve always wanted to see in an app?

My hope is to craft an experience that matches the curiosity of lifelong math learner. And in thanks for your help, I’m planning to offer promo codes so you can unlock paid content in the app once we add such functionality 😃

Feel free to comment with any ideas.
P.S. If you have any favorite niche topics—like prime numbers, exotic geometry — please mention them. I want to ensure we fill in the exact gaps you’re interested in!

[Kassander]

I'm not sure if this will help you, but I have developed a new representation for prime numbers. To be precise, the composite numbers are represented, which also makes the prime numbers visible. As I have described in my publications, this reveals new patterns that can be of importance for prime number research.

https://www.academia.edu/126146000/A_Novel_Visual_Representation_of_Prime_Number_Distribution_Interval_Graphic_Foundation_for_Further_Studies_

The special thing about this graphic, which I have called " Interval-Graphic", is that it combines many theories about prime numbers. On the one hand, it works in a similar way to the Sieve of Eratosthenes, which gradually eliminates more and more multiples of prime numbers and thus makes smaller prime numbers visible. On the other hand, Euclid's primorial and the Euclidean numbers around it can be made clearly visible. Prime number tuples such as twin primes are also visible in this way. It also becomes clear how they are created. Dirichlet's theorem is also visible, as are prime number gaps.

[Genady]

Since beauty is in the eye of the beholder, it cannot be shared. So, what is the purpose of this app?

[fooz]

18 hours ago, Genady said:

Since beauty is in the eye of the beholder, it cannot be shared. So, what is the purpose of this app?

I understand where you're coming from—beauty is indeed subjective. However, the purpose of this app is not to define beauty for others, but to guide users in discovering it for themselves.

Not everyone immediately grasps the beauty of impressionism, for example, but with the right guidance and context, they may begin to see it. Similarly, this app creates pathways for users to appreciate mathematics.

I hope this clarifies the purpose! 😊

23 hours ago, Kassander said:

I'm not sure if this will help you, but I have developed a new representation for prime numbers.

Thanks Kassander. I definitely see how your work can be converted into an interactive widget!

[Kassander]

13 minutes ago, fooz said:

Thanks Kassander. I definitely see how your work can be converted into an interactive widget!

I'm delighted to hear that you found my work useful. If you have any further questions or would like to discuss it in more detail, please don't hesitate to reach out. As the title suggests, there is still more to be published on this topic.

[Genady]

3 hours ago, fooz said:

this app creates pathways for users to appreciate mathematics

OK. Good luck!

[Genady]

Re 'math for masses'...

What do you think about this elementary math question:

(Student's answer to math question sparks discussion after teacher marks it as incorrect - Scoop Upworthy)

[TheVat]

The teacher seems to miss that what is actually pictured is a partial disk and not a semicircle.  A semicircle has no corners, but a partial disk clearly does.  A straight line meets a curved line - that is a corner.  Humans are very visual, and will respond to what an image conveys.  This tendency should work in the student's favor, not to cause confusion over the wording.  

[Genady]

But the question was about "a semi-circle." It's a math question. It is rather a student who "seems to miss that what is actually pictured is a partial disk and not a semicircle."

[studiot]

Just now, TheVat said:

The teacher seems to miss that what is actually pictured is a partial disk and not a semicircle.  A semicircle has no corners, but a partial disk clearly does.  A straight line meets a curved line - that is a corner.  Humans are very visual, and will respond to what an image conveys.  This tendency should work in the student's favor, not to cause confusion over the wording.  

I certainly agree.  +1

In any mathematics course I have ever attended a question in which the provided diagram did not match the wording would be considered ill posed and void.

 

I have seen 'trick' questions like this in psychologcal evaluations though.

But of course the evaluator is not interested in the real answer, just the reaction of the candidate.

[KJW]

9 hours ago, Genady said:

Re 'math for masses'...

What do you think about this elementary math question:

(Student's answer to math question sparks discussion after teacher marks it as incorrect - Scoop Upworthy)

One thing that was not mentioned was what the student was taught prior to being given this question.

 

[Genady]

Being misled by a visual is not a necessary condition for answering the question wrong, evidently. For an experiment, I gave the question, with no diagram, to AI:

How many corners does a semi-circle have?

 

AI has picked this answer:

 

A semicircle is a two-dimensional shape that represents half of a circle. It is formed by cutting a whole circle along its diameter.

When considering the number of corners (or vertices) a shape has, we typically look for points where two straight edges meet. A full circle has no straight edges and thus no corners. However, a semicircle includes the diameter as a straight edge.

Here's the breakdown:

• The curved part of the semicircle is smooth and has no corners.

• The straight edge (the diameter) connects two endpoints.

Therefore, a semicircle has two corners, which are the two endpoints of the diameter. These points are where the straight edge meets the curved edge, forming vertices.

 

 

 

[Genady]

16 hours ago, KJW said:

One thing that was not mentioned was what the student was taught prior to being given this question.

 

I don't know why it would matter, unless they were taught something wrong.

I also don't see anything tricky about the question. They are given a figure, which consists of a semicircle, a line, and an area, and they need to answer the question about the semicircle.

[studiot]

11 hours ago, Genady said:

Being misled by a visual is not a necessary condition for answering the question wrong, evidently. For an experiment, I gave the question, with no diagram, to AI:

 

Just now, Genady said:

I don't know why it would matter, unless they were taught something wrong.

I also don't see anything tricky about the question. They are given a figure, which consists of a semicircle, a line, and an area, and they need to answer the question about the semicircle.

 

Clearly there is a glitch in the translation from Russian to Emglish.

A trick question (which is what is I said) is designed to mislead or trick.

A tricky question is more simply a difficult one in some way.

So I repeat my assertion that any intention to mislead would be challengeable in English.

 

11 hours ago, Genady said:

 

AI has picked this answer:

...

Your AI (or LLM ) is just plain incorrect.

12 hours ago, Genady said:

It's a math question.

It is indeed a maths question not general parlance, and was posted as such.

 

Quote

https://en.wikipedia.org/wiki/Semicircle#External_links

In non-technical usage, the term "semicircle" is sometimes used to refer to either a closed curve that also includes the diameter segment from one end of the arc to the other or to the half-disk, which is a two-dimensional geometric region that further includes all the interior points.

However in mathematics

Quote

O. C.

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, π radians, or a half-turn).

 

Incidentally it was too difficult to access your scoop link.

 

[Genady]

7 minutes ago, studiot said:

AI (or LLM ) is just plain incorrect.

Not only its answer is wrong, but also its first statement:

Quote

A semicircle is a two-dimensional shape

because a semicircle is rather one-dimensional.

 

Incidentally, I've just read that this AI, DeepSeek,

Quote

matches OpenAI’s most powerful available model

(Tech leaders respond to the rapid rise of DeepSeek | VentureBeat).

So, they are all that bad.

 

P.S. It seems that you think I brought the AI answer as a correct one. Clearly, there is a miscommunication, because my intent was exactly opposite.

P.P.S. I make mistakes in English from time to time, but I do not translate from Russian. 

[KJW]

4 hours ago, Genady said:

20 hours ago, KJW said:

One thing that was not mentioned was what the student was taught prior to being given this question.

I don't know why it would matter, unless they were taught something wrong.

It matters because the student was expected to know the correct answer and therefore should have been taught how to correctly answer the question. As I see it, answering the question is simply a matter of knowing a definition, and therefore marking the student wrong if the definition was never taught is wrong.

How many people know that a circle is just the perimeter and doesn't include the area inside? Or that a sphere is just the surface and does not include the volume inside? It seems like a subtle point to require the student to know unless it had been explicitly taught. And if the student was taught this, then the student should have correctly answered the question. But here we are debating the answer to the question (which is simply based on a definition) without the context of what the student was taught.

 

Edited 12 hours ago by KJW

[Genady]

3 minutes ago, KJW said:

It matters because the student was expected to know the correct answer and therefore should have been taught how to correctly answer the question. As I see it, answering the question is simply a matter of knowing a definition, and therefore marking the student wrong if the definition was never taught is wrong.

How many people know that a circle is just the perimeter and doesn't include the area inside? Or that a sphere is just the surface and does not include the volume inside? It seems like a subtle point to require the student to know this unless it had been explicitly taught. And if the student was taught this, then the student should have correctly answered the question. But here we are debating the answer to the question (which is simply based on a definition) without the context of what the student was taught.

 

Do you think it is possible that they ask a question in a math test about something that has not been defined?

[KJW]

21 minutes ago, Genady said:

Do you think it is possible that they ask a question in a math test about something that has not been defined?

Of course it is possible, but how likely it is I cannot say. However, prior to my first post, I did look at the link to check if this question was indeed part of a maths test rather than simply a textbook exercise, and could find no indication of which it is. I checked because I wanted to know the cost to the student of getting the question wrong, and therefore the importance of having been given the definition prior to the question.

 

[Genady]

10 minutes ago, KJW said:

Of course it is possible, but how likely it is I cannot say. However, prior to my first post, I did look at the link to check if this question was indeed part of a maths test rather than simply a textbook exercise, and could find no indication of which it is. I checked because I wanted to know the cost to the student of getting the question wrong, and therefore the importance of having been given the definition prior to the question.

 

Fair enough.