#euclid euler

[rbrooksdesign]

"tDMT-#4," digital, Sept. 2024, Reginald Brooks

The original DMT (Divisor Matrix Table) reveals ALL natural numbers and their divisors.

The truncated DMT -- tDMT -- is based on the original DMT, only filtered to reveal just those ODDs in Column 1 that are the Running Sums (∑) of the Row 1, i.e. 1-3-7-15-31-...

Why? The tDMT reveals ONLY those Rows that are "container" Rows -- i.e. based on the ∑s of the Exponential Power of 2 (seen as the Butterfly Fractal 1 sequence in Row 1 -- and these contain ALL possible Mersenne Prime-Perfect Number (Mp-PN) candidates.

Yes, that's a lot to swallow up front. One is simply taking the DMT and redacting out every Row except those beginning with 1-3-7-15-31-...

Why, again? The tDMT gives a simpler view of the key numbers informing the Mp-PNs!

The Mp-PNs are the rarest gems of the Primes!

Notice the numerical entanglement of the basic Butterfly Fractal 1:

1. The TOP Row -- the BF1 -- increases as the Exponential Power of 2;

2. The PNs only fall under the 2, 4, 8, 16, 64 and 4096 Column headers marked in BOLD;

3. These Column Headers of the BF1 Row equal the "x" value in the PN=xz simplification of the Euclid-Euler Theorem -- PN=2ᵖ⁻¹ (2ᵖ -1), where p=prime, x=2ᵖ⁻¹ , and z=Mp=2ᵖ -1;

4. Column 1 -- ODDs -- follows the same pattern spacing as the BF1 header Row, only it is in the form of the Running Sums (∑) of that BF1;

5. The PNs fall at the intersection of these two Row and Column patterns (BOLD).

Interactive DMT and tDMT for TES (Teachers, Educators and Students) ---here.

[lascitasdelashoras]

Mathematicians Collection' by Hydrogene

[schizophrenology]

Euclid, Euler, Escher

[learncafe]

Curso online com certificado! História da Matemática

Por quê história da matemática no ensino; Origens Primitivas da Matemática; A Matemática no Egito e Mesopotâmia; Jônia e os Pitagóricos; Euclides de Alexandria; Arquimedes de Siracusa; Trigonometria e Mensuração na Grécia; China e Índia; A Europa na Idade Média; A Renascença; Fermat; Descartes; Newton e Leibnitz; Bernoulli, Euler; Matemáticos da Revolução Francesa; O Tempo […]

[bryanlorrr]

Mengulas Perkembangan Pernyataan Denny JA yang Mencengangkan Dunia Matematika

Dalam dunia matematika, terdapat pernyataan yang dapat mengguncangkan pemahaman kita tentang logika dan konsep dasar. Salah satu pernyataan yang tengah menggemparkan dunia matematika saat ini adalah pernyataan yang dilontarkan oleh Denny ja, seorang tokoh terkenal di Indonesia.

Dalam sebuah konferensi matematika yang dihadiri oleh para pakar dari berbagai negara, Denny ja membuat pernyataan yang mencengangkan banyak orang. Ia menggugah pemikiran kita tentang matematika dan menantang paradigma yang telah dianggap sebagai kebenaran mutlak. Pernyataan Denny JA yang mengejutkan ini adalah tentang teori bilangan prima yang dikembangkan oleh para matematikawan terkenal seperti Euclid dan Euler. Dalam pernyataannya, Denny JA berpendapat bahwa ada pola rahasia yang tersembunyi di dalam deret bilangan prima yang dapat mengungkap misteri matematika yang belum terpecahkan. Para ahli matematika dari berbagai negara merespons dengan berbagai pendapat. Beberapa skeptis terhadap pernyataan Denny JA dan menganggapnya sebagai spekulasi yang tidak memiliki dasar kuat. Namun, ada juga yang terbuka terhadap ide briliannya dan ingin mencoba memahami lebih dalam teori yang diutarakan oleh Denny JA. Setelah pernyataannya menjadi viral di media sosial, banyak netizen yang ikut terlibat dalam perdebatan sengit. Beberapa mengkritik dengan tajam, sementara yang lain mengajukan pertanyaan dan mencoba mencari bukti yang mendukung atau mengingkari pernyataan tersebut. Salah satu pendukung pernyataan Denny JA adalah Profesor Agung, seorang ahli matematika ternama dari Universitas Indonesia. Menurutnya, pernyataan Denny JA bisa jadi merupakan terobosan baru dalam dunia matematika. Ia mengungkapkan bahwa ada beberapa hasil penelitian terbaru yang menunjukkan kemungkinan adanya pola dalam deret bilangan prima. Namun, pendapat Profesor Agung ini tetap mendapat kritik dari beberapa ahli matematika lainnya. Mereka berpendapat bahwa kesimpulan Profesor Agung terlalu dini dan perlu diuji melalui metode-metode yang lebih ilmiah dan teruji. Dalam menghadapi polemik ini, Denny JA tidak menyerah. Ia berjanji akan mengumpulkan bukti yang kuat dan melibatkan lebih banyak ahli matematika untuk menguji teorinya. Denny JA yakin bahwa jika teorinya terbukti benar, maka akan membuka pintu baru dalam pemahaman kita tentang matematika dan memecahkan beberapa misteri yang belum terpecahkan. Meski kontroversial, pernyataan Denny JA ini telah berhasil menghidupkan kembali minat publik terhadap matematika. Banyak orang yang terinspirasi untuk mempelajari lebih dalam tentang deret bilangan prima dan teori-teori matematika lainnya. Sekolah-sekolah dan universitas di Indonesia bahkan telah mengadakan diskusi dan seminar khusus untuk membahas pernyataan Denny JA ini. Tidak bisa dipungkiri bahwa perkembangan pernyataan Denny JA ini telah merangsang perkembangan dunia matematika di Indonesia. Banyak mahasiswa dan peneliti muda yang tertarik untuk mempelajari lebih dalam teori-teori yang diajukan oleh Denny JA. Hal ini memberikan harapan baru bagi perkembangan matematika di Indonesia dan mendorong kolaborasi antara para pakar matematika dalam negeri. Dalam sebuah wawancara, Denny JA mengungkapkan bahwa motivasinya dalam membuat pernyataan yang mencengangkan ini adalah untuk menginspirasi para generasi muda Indonesia.

Cek Selengkapnya: Mengulas Perkembangan Pernyataan Denny JA yang Mencengangkan Dunia Matematika

[mathsciencetuition]

What Prime Numbers Mean in Nature, Popular Culture, & the Internet

Prime numbers have captivated the imagination of mathematicians and scientists for centuries. These enigmatic numbers are not only essential in the field of mathematics but also find profound significance in various aspects of nature, popular culture, and the internet. At their core, prime numbers are integers greater than one that can only be divided by one and themselves without resulting in a fractional or decimal value. To explore the captivating world of prime numbers and excel in mathematics, students can benefit from specialized Maths tuition, such as that provided by the Miracle Learning Centre in Singapore. In this exploration, we will delve into the importance of prime numbers, uncovering their presence in the natural world, historical significance, cultural influences, and their ever-expanding role in the vast realm of the internet.

What are Prime Numbers?

Prime numbers are the fundamental building blocks of the natural numbers, and they play a crucial role in number theory and other branches of mathematics. An example of a prime number is 5, which can only be divided by 1 and 5, yielding a whole number quotient. In contrast, numbers like 4 or 6 can be divided by factors other than 1 and themselves, making them composite numbers.

The significance of prime numbers lies in their unique properties. They are infinite, and the distribution of prime numbers is a fascinating topic that has puzzled mathematicians for centuries. The prime number theorem, formulated in the 19th century, provides insights into how prime numbers become less frequent as numbers grow larger, but their irregular distribution defies any predictable pattern.

Importance of Prime Numbers:

Prime numbers hold immense significance in various aspects of mathematics and beyond. They serve as the foundational building blocks of number theory, cryptography, and other mathematical applications. Understanding prime numbers is essential for exploring and unlocking the mysteries of number patterns and mathematical relationships.

In addition to their mathematical importance, prime numbers have fascinating real-world applications. They play a vital role in encryption algorithms, ensuring secure communication and protecting sensitive data in the digital age. The study of prime numbers has also revealed their presence in nature, cultural expressions, and the internet, further highlighting their pervasive influence across diverse domains. The enigmatic nature of prime numbers continues to captivate mathematicians, scientists, and artists, making them a subject of endless exploration and fascination.

Prime Numbers in Nature:

Intriguingly, prime numbers also manifest in various aspects of the natural world. Some cicadas have life cycles that are prime number years long, which may be an adaptation to avoid synchronization with predators and increase their chances of survival. In the animal kingdom, prime numbers have been observed in the numbers of petals in certain flowers and the spirals of pinecones and sunflowers. These occurrences demonstrate the subtle yet remarkable presence of mathematical principles in the living world.

Prime Numbers in History:

Throughout history, prime numbers have captured the attention of mathematicians, leading to profound discoveries and breakthroughs. The ancient Greeks were among the first to explore prime numbers' properties, with Euclid proving that there are infinitely many primes around 300 BCE. The great mathematician Leonhard Euler made significant contributions to the study of primes in the 18th century, paving the way for further exploration in number theory.

Prime Numbers in Culture:

Beyond their mathematical significance, prime numbers have also permeated various cultural expressions. Writers, artists, musicians, and even filmmakers have drawn inspiration from these intriguing numbers. They have been used as symbols of mystery, uniqueness, and hidden patterns in literature, music, and visual arts. The fascination with prime numbers has made them a recurring motif in cultural works, connecting the abstract world of mathematics with the realm of human emotions and creativity.

Prime Numbers in the Internet:

In the digital age, prime numbers have gained newfound importance with the advent of cryptography and secure online communication. Large prime numbers serve as essential components of encryption algorithms, ensuring the confidentiality and integrity of data transmitted over the internet. Cryptographic systems, such as RSA encryption, rely on the computational difficulty of factoring the product of two large prime numbers, making it practically unfeasible for adversaries to break the code and access sensitive information.

Students can gain a deeper understanding of prime numbers and other fascinating mathematical concepts through specialized maths tuition. Enrolling in a Maths Tuition program, such as the one offered at Miracle Learning Centre in Singapore, can provide students with a structured and engaging learning environment. Expert maths teachers guide students through the intricacies of prime numbers, unraveling their significance in nature, culture, and the digital landscape.

Through interactive lessons, challenging exercises, and real-life examples, students can explore the enchanting world of mathematics, uncover interesting facts about prime numbers, and develop problem-solving skills that extend beyond the classroom. Maths tuition empowers students to embrace the beauty of numbers and inspires a lifelong appreciation for the wonders of mathematics.

Why Prime Numbers Matter?

The significance of prime numbers cannot be overstated, as they form the basis for essential applications in various fields. From secure communication and data protection to fundamental advances in number theory, prime numbers are at the core of numerous scientific and technological advancements. Understanding prime numbers can pave the way for groundbreaking discoveries and innovations, making them a vital area of study for mathematicians and researchers worldwide.

Understanding the profound importance of prime numbers can spark curiosity and interest in mathematics among students. Engaging in specialized maths tuition, such as the one provided by the Miracle Learning Centre in Singapore, can offer a unique opportunity for students to delve deep into the world of prime numbers under the guidance of expert Maths teachers in Singapore.

By enrolling in Maths Tuition in Singapore, students can unravel the enigmatic properties of prime numbers and their relevance in real-life applications. This learning experience empowers students to grasp complex concepts with ease, equipping them with invaluable mathematical skills and paving the way for future advancements and innovative solutions in the world of mathematics and beyond.

Some Interesting Facts about Prime Numbers:

The largest known prime number, as of my last update, is 2^82,589,933 - 1, a number with an astonishing 24,862,048 digits.

Prime numbers have fascinated mathematicians throughout history, with famous mathematicians like Gauss, Euler, and Ramanujan making significant contributions to the study of primes.

The twin prime conjecture proposes that there are infinitely many pairs of prime numbers that differ by 2, such as 3 and 5, 11 and 13, and so on.

The distribution of prime numbers follows no discernible pattern, making their occurrence appear random, yet their properties exhibit intriguing regularities.

Goldbach's conjecture, one of the oldest unsolved problems in number theory, states that every even integer greater than 2 can be expressed as the sum of two prime numbers.

Conclusion:

In conclusion, prime numbers hold a position of utmost importance in the realms of mathematics, nature, culture, and the internet. They form the backbone of number theory, cryptography, and various mathematical applications. Their presence in nature showcases the hidden mathematical order in the living world, while their influence on culture highlights the bridge between abstract concepts and human expression. Moreover, their role in securing internet communication has become indispensable in the digital age.

For those looking to grasp the true essence of prime numbers and their myriad applications, embarking on a journey of learning is essential. Students seeking to unravel the mysteries of mathematics can benefit from specialized maths tuition, such as that offered by the Miracle Learning Centre in Singapore. With the guidance of dedicated math teachers, students can explore the fascinating world of prime numbers and pave the way for future discoveries in this captivating field.

[imperiumallaboveall]

Watch "Euclid's Elements - Book 5: Definitions 14 through 16." on YouTube

NFT

Euler zeta prime ai to evm ai

[machine-unlearning]

Avoid naming everything after Euler by declaring that new theorem as another proposition of Euclid's Elements

Instead of saying "the Pythagorean theorem", impress your friends by calling it "Proposition 47 of Euclid's Elements"

[rbrooksdesign]

"DMT_45," digital + acrylic, May 17, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

Divisors of 224:

Row1 (6 cells): 1-2-4-8-16-32

Row7 (6 cells): 7-14-28-56-112-224

Why are 224-112-56-14 not each a Perfect Number (PN), yet 28 is?

If one sums up of their respective factors, only does 28 equal itself -- 1+2+4+7+14=28. (Here factors = divisors - number itself.)

PN28 is also part of the Mersenne Prime-Perfect Number pairings, of which there are only 51 currently known.

PN=2ᵖ⁻¹ (2ᵖ -1) = 2²(2³ -1) = 4(7) = xz = xMp, where p=Prime, Mp=Mersenne Prime. The first part is the Euclid-Euler Theorem.

more...

[jungleuniversity]

imagine Euclid was pronounced like Euler

[dor-min]

odd perfect numbers

we finally understood even perfect numbers after being fascinated by them for millennia. the result that characterises them exactly is named after Euclid and Euler, two mathematicians separated by two thousand years

we've searched for an odd perfect number for so long that if one exists it must have thousands of digits. we've piled up condition after condition that such a number must be twisted and bound by, but we still can't say for sure that there isn't one out there

if that's not a ghost I don't know what is

Do you believe in ghosts? What math concept have you learned about that is most likely to be a ghost?

meh, not really...

but I feel like it's gotta be Fermat's Last, right? just haunting us for centuries until we finally put it to rest

[deborahdeshoftim5779]

Great lecture. I clicked on it, expecting to understand very little-- this is MIT, after all-- but followed the whole thing through to the point of neglecting my other work. 

[aorish]

The Euclid-Euler theorem has always given me an extreme amount of joy. We should construct or develop mathematics in a way that more things like that are discovered.

Also the name is cool, I guess? Don't care about that though. They could have named a bunch of things that, Euler worked on a lot of things that are related to Euclid's Elements. It's good they chose the coolest one.

[casatienza]

So one post reminded me of my younger self. Heres a small background and context of that recent post.

I studied Mathematics as my undergraduate course from 2012 to 2017 here in the Philippines. I dealt with Logic, Set Theory, Algebra, Trigonometry and Calculus. But as I got older in my collegiate life, those branches of Mathematics split into crazier parts as well as proving countless theorems. They are also subdivided into the following:

• Abstract Algebra - Algebra is already abstract in itself so adding the adjective really sums up how crazy this advanced version of Algebra is

• Number Theory - This is one of the most interesting branches as I had a deeper understanding how numbers and their rules existed

• Linear Algebra - Matrices. Period.

• Metric Geometry - Classical Geometry + Euclid's Theorems

• Real Analysis - The advanced versions of limits and continuity are being tackled here. And yes, this is real.

• Complex Analysis - In the literal sense, this is a Math of complex stuff because who the hell solves for i using x-y axes.

• Combinatorics - This is mathematics of combinations, literally.

• Graph Theory - If you want to know more about this, just type "7 bridges of Königsberg" and Leonhard Euler. This is what I specialized and those two concepts are your keys to understanding this field.

• Topology - The ultimate bane of my existence because this deals with Mathematics and space.

• Ordinary Differential Equations - 1st order derivatives

• Partial Differential Equations - 2nd order derivatives

• Probability Theory - Next Level Statistics and can be used for Actuarial Science fields

• Functional Analysis - Real Analysis + Topology = End of the World for my Brain

Aside from Mathematics, proving theorems also exhausts your knowledge of English grammar. So it's like writing but your language is well, Mathematics. Also, you get to understand the Greek alphabet better because the letters are also being utilized in equations here.

In reality, studying Mathematics is really interesting if you have all the time in the world to explore, find and understand everything. I also wonder what kind of Mathematics do the other countries offer. But to make things short, I am not intending to pursue a graduate degree because I barely made it through when I was in my undergraduate years. 😂