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Mathematician here.
This is a common type of trick question.
The bar must be cut into 15 pieces, but that doesn't mean 15 cuts.
The bar is already 1 big piece, with 0 cuts.
1 cut results in 2 pieces.
2 cuts result in 3 pieces.
3 cuts result in 4 pieces.
And so on, with n cuts resulting in n+1 pieces.
Hence, 14 cuts result in 15 pieces.
14 cuts are needed.
The error of assuming 15 cuts, is one of the most common errors in mathematics and computer programming, called the Fence Post Error. It's the error of mixing up the number of boundaries, segments, and cuts.
See my lecture in the comments, for more details about the Fence Post Error.
My lecture on the Fence Post Error.
One of the most common errors in mathematics and computer programming.
It's the error of mixing up the number of boundaries, segments, and cuts.
Enjoy!
youtu.be/MZNA91zzSPI?si=rJg7…
121
Mathematician here to explain.
On a spherical surface, a triangle can have 3 right angles.
For example, consider a triangle between the following 3 points on the Earth surface:
The north pole, and 2 point along the equator between which the distance is ¼ of the Earth's circumference.
All 3 angles will be 90º.
Mathematician here.
If the doubling dollar is also tax free, push the Red button.
You'll get $1 Billion in 30 months, which is 2.5 years. You'll get $2 Billion the next month after that.
The amount received after t months, is given by the formula:
A = 2^t
2³⁰ = 1,073,741,824
BUT...
If it's not tax free, the government will be getting that cash at an exponential rate as well, and will likely start spending it at an exponential too.
Such influx of cash into the economy would lead to exponential inflation, reducing much of your purchasing power.
So, if the doubling dollar is taxed, push the Green button, and enjoy your tax free Billion.
Mathematics.
Green button = You instantly receive $1 billion (tax free).
Red button = You receive $1 that doubles every month.
You can press just once. Which do you press?
30
The age of consent debate, has to do with math and physics education throughout history.
As technology advanced, the amount of mathematical and technical knowledge required to function in the world, increased.
As a result, it now takes more years of education to prepare a person for adulthood in general, and for parenthood in particular.
From that perspective, it makes sense for more technologically advanced societies to have a higher age of consent... and perhaps a higher voting age too.
The puzzle, is what to do about biology staying the same, while technology advances. This has always been a puzzle for humanity, and the answer probably involves more efficient education.
In the UK, the legal age of consent is 16, which means that an adult can legally have sex with a 16- or 17-year-old.
The legal age of consent needs to be raised to 18. We should never encourage or allow adults to have sex with children.
Children in the UK are legally classed as children until they reach the age of 18.
So why does the law allow adults to have sex with 16- and 17-year-olds?
It’s time to close this gap in the law and put the protection of children first. Raise the age of consent to 18.
Fun fact:
Friday the 13th has happend 3 times in 2026.
February, March, and today in November.
Every year has at least 1 Friday the 13th, and at most 3, due to the structure of the calendar.
The last year to have 3, was 2015. The next year to have 3 will be 2037.
1
102
Those aware of Star Wars Ring Theory, will have a special appreciation for this logo.
Notice the 5 and the 0 are designed to look like rings with a gap, used in the common interlocking rings magic trick.
Star Wars Ring Theory is that The George Lucas Star Wars movies "rhyme," and have cyclical elements, like verses and a chorus in a piece of music.
For example:
A New Hope starts and ends with a space battle.
The original trilogy starts and ends with destroying a Death Star.
The Phantom Menace starts with the main character's boarding a RING shaped ship near Naboo, and ends with the same type of ship being destroyed near Naboo. That destruction also "rhymes" with the destruction of the Death Star in episodes 4 and 6. Like a repeating chorus. Tatooine is also part of that same chorus, where many events happen there in episodes 1, 4, and 6.
The prequel trilogy starts with Anakin building a droid and being separated from his mother (who later dies), and Obi Wan losing his master. It ends with Anakin becoming part machine himself and being separated from his wife (who later dies), and Obi-Wan Wan losing his apprentice.
The entire 6 film saga starts with Anakin meeting Obi Wan and Yoda early in his life, and ends with Anakin meeting Obi Wan and Yoda as a ghost, early in his afterlife.
The films are like magic interlocking rings, that can seamlessly transform between being separate films, and being one long interconnected structure. They are also like rings due to repeating patterns in the story. And they connect generations of fans. All that is part of the magic of Star Wars.
Many criticized the sequel trilogy as "feeling off," as if the films could be okay sci-fi movies in a separate universe, but are bad Star Wars movies. What people were likely feeling, was that the rhythm and rhyme, if there were any, didn't match the first 6 films. The ring patterns weren't there, or were distorted.
Sure, episode 7 had a desert planet and something like a Death Star, but the planet wasn't Tatooine, and we just had that in episode 6. It's like the chorus played twice back to back, without a verse in between, and some of the notes were off the 2nd time around.
Sure, the sequels end on Tatooine, but the Skywalker bloodline also ends (unless Rey is secretly pregnant) and the Palpatine bloodline wins.
The "music" of the story was off.
I wonder if Star Wars Ring Theory played a role in the inspiration for the 50th anniversary logo design.
To those interested in a more mathematical comparison of all Star Wars movies and shows, see my lecture below.
It analyzes critics scores and audience scores of all Star Wars movies and shows, up to and including The Mandalorian and Grogu.
youtu.be/QSBvYFasfKY?si=Q8sy…
34
"It's the time you spent on your rose that makes your rose so important... People have forgotten this truth, but you mustn't forget it. You become responsible forever for what you've tamed. You're responsible for your rose."
-Antoine de Saint-Exupéry, The Little Prince
“No one cares about your homebrew.”
I hate that crap. This entire hobby was built on folks making stuff up, tinkering with rules, and sharing their ideas.
Try having an imagination for once.
And to everyone out there making their own stuff, keep at it. We want to hear about it.
46
Many are familiar with the mathematical symbol:
Σ
Used for summation of terms defined to its right.
A lesser known symbol is:
Π
Used for the product of factors defined to its right.
Σᵢ₌₁⁵(i) = 1+2+3+4+5
Πᵢ₌₁⁵(i) = 1×2×3×4×5
Σ is the upper case Greek sigma, ancestor of the Latin S and Cyrillic С, and descendant of the ancient Hebrew ש.
Π is the upper case Greek pi, ancestor of the Latin P and Cyrillic П, and descendants of the ancient Hebrew פ.
That works, except n would have to start with 3.
It would then simplify to:
Π_3 ^100 ( (n-1)/n ) = (3-1)/100
= 2/100
39
Long summations are often simplified by finding terms that cancel out via subtraction.
Long products are often simplified by finding factors that cancel out via division.
These are both very powerful tools, and useful to look for. They can turn a seemingly impossible problem into a very simple one. Hence the term:
"Simplification"
Mathematician here.
Simplify each bracket.
(2/3)(3/4)(4/5)...(98/99)(99/100)
= (2×3×4×...×99) / (3×4×5×...×100)
Everything cancels out except 2 in the numerator and 100 in the denominator.
So, it simplifies to:
2/100 = 1/50 = 0.02
26
Visual proofs are a philosophical concept, as much as they are a mathematical tool.
A visual proof is often more intuitive than a standard proof.
In day to day life, showing something is often much more powerful than explaining it.
The reason humans have to be taught to not judge everything based on looks, is because we evolved to judge things based on looks. We evolved this way because it can often save time and resources that would be necessary for a more thorough analysis. In some situations, time and resources are scarce, and a quick descision is needed. Humans' love of visual proofs, is likely a result of this evolutionary phenomena.
For those interested in more details about the Difference of Squares formula, and how it's proven, see my lecture here:
youtu.be/0aSponh-QRE?si=JfNO…
21
This post is getting a lot of attention.
The solution it presents is an excellent example of how knowing some common algebraic relations, can make difficult looking problems turn into very simple ones.
When it comes to computer programming, use of these kinds of relations can significantly reduce processing time.
Mathematician here.
The solution uses the Difference of Squares formula:
a² - b² = (a+b)(a-b)
a = 2024
b = 1
2024² - 1 = 2024² - 1²
= (2024 + 1)(2024 - 1)
= (2025)(2023)
So, the question becomes:
√(2025×2023/2023) = √(2025)
= 45
26
Star Wars is a story written by George Lucas.
Star Wars stories written by anyone else, are fan fiction. Canon or not, good or bad, it's still fan fiction.
2
3
233
Mathematician here.
The solution uses the Difference of Squares formula:
a² - b² = (a+b)(a-b)
a = 2024
b = 1
2024² - 1 = 2024² - 1²
= (2024 + 1)(2024 - 1)
= (2025)(2023)
So, the question becomes:
√(2025×2023/2023) = √(2025)
= 45
For those interested in more details about the Difference of Squares formula, and how it's proven, see my lecture here:
youtu.be/0aSponh-QRE?si=JfNO…
Mathematician here to burst your bubble.
A square is a rectangle with 4 sides of equal length.
A rectangle is a parallelogram with all angles 90º.
A parallelogram is a 4-sided shape consisting of 2 pairs of parallel sides.
The image quoted below is not a parallelogram.
If you need to be convinced of that:
It doesn't have 4 sides. On the circular curves, it has infinitely many sides. It also has infinitely many pairs of parallel sides opposite each other on those curve, not just 2 pairs.
If it's not a parallelogram, then it's not a rectangle. If it's not a rectangle, then it's not a square.
