https://youtu.be/8d7iFNthPBg

https://www.freecodecamp.org/learn/coding-interview-prep/project-euler/problem-148-exploring-pascals-triangle

Simply replace "return true" with "return 2129970655314432;"

i before e, except after c.

In this post:

https://towardsdatascience.com/experimental-math-in-the-age-of-data-science-d6ae666c7017

So I messing around on desmos.com/geometry and found this triangle center. Here is how it is constructed:

Given Triangle ABC, draw circles centered at each vertex with a radius equal to the length of the corresponding median. Draw a secant line everywhere the circles intersect. Where the secant lines intersect is your triangle center. See at: https://www.desmos.com/geometry/lxebef3xdk

It appears to lie on the Euler line of ABC. See at: https://www.desmos.com/geometry/slsbhtqxao I can't find what it is called. I assume it has already been discovered since the construction is so simple. If someone could please tell me what it is called, it would be much appreciated. Thank you.

I read about Euler lines today and noticed something interesting about all of the diagrams showing the Euler line on triangles. It looked as if the Euler line always "cut" the triangles into two shapes of equal area. I know that the line will cut isosceles triangles in half because it bisects the angle where the two legs of the triangle meet.

Naturally I tried looking up if this is actually a thing, but couldn't find any results whatsoever.

Is there any truth to the statement that any triangle's Euler line will always divide the triangle into two shapes of equal area?

...where k = n, and I thought of this:

For every n>=1, does there exist a set of solutions a*1, a2... an, b for each n such that the sum a1n* + a*2n+...+ann* = b^n ? i.e. is it true there exists such a set for all n?

Has anyone answered this with a definitive yes or a no?

EulerPy is a small Python package I've been working on to make it easier to work through Project Euler problems in Python. It handles both the creation of "template files" containing the problem text as a docstring and also checking the output of each file to verify if it outputs the correct solution or not. Given the fact that many people learning how to program are pointed towards Project Euler, I figured /r/learnprogramming might be interested.

This is my first ever Python package, so hopefully I didn't do anything too catastrophically wrong, considering I'm still fairly new to this stuff. I wrote more about the development in more detail on my blog.

One of those cases where you think you're trying to do something simple and it turns out you're not!

All I'm trying to do is get a MPU-6050 to measure its angle from level on the x and y planes. So, essentially, pitch and roll. The board is static, should not be subject to vibration and I'm interested in changes over a long period of time. Therefore, I figure I should be able to just use accelerometer readings over a second or two and either filter and take a mean, or just take a mean for a reasonably accurate measure since the only force should be gravity, no need to worry about gyros.

I think I want the euler angles, not yaw, pitch, roll since the latter are for moving objects and the drift I see makes them useless for my measuring. I've tried to hack the code, but only managed to output NANs. Can anyone with some experience with FreeIMU give me some help? I'm totally lost.

So I have to prove that point F (4, -4/5) lies on the line y=1157/3080x - 6551/3080. I've tried solving this and it turns out it doesn't. Can anyone else verify that it does or doesn't? I think it may be because of the rounding I did through decimals and such. Much appreciated!

is it just a mathematical curiosity, or is there some actual practical application for it? (or building block for some other mathematical concepts)

Some of you may have seen my previous post, but I settled to have a project on the Euler's Line. I found out that as long as one corner of the triangle is stationary, the positions of the orthocenter and circumcenter relative to the position of the centroid vary, depending on how far the other two corners stretch. If they get closer, the orthocenter is below the centroid and the circumcenter is above the centroid. If the two corners get away from one another, the opposite. Using this idea, I could measure the relative areas of triangles, looking at the positions of the circumcenter and orthocenter.

But here is my problem. It is too simple. I only get to measure the points the circumcenter and orthocenter are, which is very simple (only involves perpendicular bisectors etc.). Any ideas how to make it more complex?

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Introduction

I did a little math to show the true power of lending and staking. I am using Celsius as an example of a LENDING platform. One can chose to stake their own coins, use lending services, yield farming, etc. This depends on risk tolerance, of course.

Example

Setting up the initial conditions:

1. You buy (or already own) 0.05 BTC (worth around $2.3k USD right now)
2. You buy 0.00001 BTC every week (worth around $5 right now)
3. You decide deposit this BTC on Celsius, earning 6.20% APY - assuming constant interest rate and Celsius remains operational through out the time period.
4. You wait until Jan 5, 2026, or 4 years from now.

Firstly, Celsius rates are in APY. Converting to APR gives ~6.018%. Weekly interest is 1.001157308x.

As shown in Figure 1, below, the blue line will be your Bitcoin balance using Celsius. The orange line is the amount of Bitcoin you bought, or the amount of Bitcoin you would have if you weren't using Celsius.

Figure 1: BTC Balance over a 4 year period

Results

By January 5, 2026, you would have bought a total of 0.0521 BTC and earned 0.013938621 BTC from interest.

In total, you would have 0.066038621 BTC.

The table below shows how much your Bitcoin will be worth in January 2026 based on the following price assumptions:

At higher prices, the interest earned has a massive effect on your overall gain.

Note: This is obviously a rough estimate. Also, your cost basis will depend on the future prices of Bitcoin.

Conclusion

In conclusion, it is evident that staking/lending is an extremely powerful tool to multiply your returns by a considerable amount. You can increase these results further by increasing your initial investment or increasing your weekly addition.

Fun

I created a fun thought experiment.

The functions generated by our example are as follows, where e is Euler's number and x is number of weeks:

y = 0.05*e^0.0013x - Exponential
y = 1E-05x + 0.05 - Linear

These functions plotted over a 45 year period:

[Figure 2: BTC Amount over a 45 Year Period](https://preview.redd.it/3121xi0i9j981.png?width=1968&format=png&auto=webp&s=b1b

Do your worst!

I'm surprised it hasn't decade.

They were cooked in Greece.