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Today's Topics:
1. One for the Numerologists and Mystics... (David)
2. Re: One for the Numerologists and Mystics... (Antony Barry)
3. US launches probe into semiconductor industry (Stephen Loosley)
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Message: 1
Date: Tue, 24 Dec 2024 21:02:36 +1100
From: David <[email protected]>
To: [email protected]
Subject: [LINK] One for the Numerologists and Mystics...
Message-ID: <2206947.irdbgypaU6@ulysses>
Content-Type: text/plain; charset="iso-8859-1"
* 2025, itself is a square, i.e. 45 x 45 = 2025
* it is also a product of two-squares, i.e. 9? x 5? = 2025
* it is also the sum of 3-squares, i.e. 40?+ 20?+5?= 2025
* and remarkably it is also the sum of the cubes, of all the single
digits, from 1 to 9, i.e.1?+2?+3?+4?+5?+ 6?+7?+8?+9?= 2025.
I didn't figure this out, I'm just passing it on, but it IS unusual!
I hope all linkers have a restful Christmas.
DavidL
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Message: 2
Date: Tue, 24 Dec 2024 21:25:54 +1100
From: Antony Barry <[email protected]>
To: David <[email protected]>
Cc: [email protected]
Subject: Re: [LINK] One for the Numerologists and Mystics...
Message-ID:
<CAECOtWzuArNcmeV_SctVmybSNVWec7844Dn_zTfxqL4B5=t...@mail.gmail.com>
Content-Type: text/plain; charset="UTF-8"
On Tue, Dec 24, 2024 at 9:05?PM David <[email protected]> wrote:
> * 2025, itself is a square, i.e. 45 x 45 = 2025
> * it is also a product of two-squares, i.e. 9? x 5? = 2025
> * it is also the sum of 3-squares, i.e. 40?+ 20?+5?= 2025
> * and remarkably it is also the sum of the cubes, of all the single
> digits, from 1 to 9, i.e.1?+2?+3?+4?+5?+ 6?+7?+8?+9?= 2025.
I asked Perplexity AI is there was anything interesting about 2025 with the
following result -
2025 indeed possesses several interesting properties that make it
noteworthy in number theory:
## Mathematical Properties
**Perfect Square**
2025 is a perfect square, specifically 45^2[1][4]. This property alone
makes it significant in number theory, as square numbers often exhibit
unique characteristics.
**Sum of Consecutive Odd Numbers**
2025 can be expressed as the sum of five consecutive single-digit odd
natural numbers: 1 + 3 + 5 + 7 + 9[3]. This property is particularly
interesting as it connects 2025 to other mathematical sequences.[Note by
Tony: Perplexity seems to have got confused!]
**Unique Squaring Property**
2025 is probably the only positive square which remains a square when
adding 1 to each digit (resulting in 3136) as well as when increasing just
the first digit (resulting in 3025)[2]. This unusual characteristic sets
2025 apart from other numbers.
## Number Theoretical Aspects
**Prime Factorization**
The prime factorization of 2025 is 3^4 * 5^2[1][6]. This decomposition into
prime factors is fundamental in number theory and contributes to many of
its other properties.
**Divisibility**
2025 has 15 divisors[1], making it a highly composite number. It is also a
tau number, as it is divisible by the number of its divisors[2].
**Special Number Classifications**
2025 falls into several interesting number categories:
- It is a Harshad number (divisible by the sum of its digits)[2].
- It is a Curzon number[2].
- It is an apocalyptic number[2].
- It is a gapful number (divisible by the number formed by its first and
last digit)[2].
## Unique Representations
**Sum of Squares**
2025 can be written as a sum of two non-zero squares in only one way: 27^2
+ 36^2[2]. This property relates to the Pythagorean theorem and Fermat's
theorem on sums of two squares.
**Sum of Consecutive Primes**
Interestingly, 2025 can be represented as the sum of five consecutive prime
numbers: 397 + 401 + 409 + 419 + 421 = 2025[7]. This connection to prime
numbers adds to its number-theoretical significance.
## Conclusion
These properties collectively make 2025 a number of considerable interest
in number theory. Its status as a perfect square, its unique
representations as sums of consecutive numbers (both odd and prime), and
its various special number classifications demonstrate that 2025 possesses
a rich set of mathematical characteristics worthy of study in number theory.
Sources
[1] Properties of the number 2025 - Number Empire
https://www.numberempire.com/2025
[2] Properties of number 2025 - Numbers Aplenty
https://www.numbersaplenty.com/2025
[3] 25 (number) - Wikipedia https://en.wikipedia.org/wiki/25_(number)
[4] Number 2025 - Math Tools https://math.tools/numbers/2025
[5] Properties of natural numbers such that there is a "very large largest
...
https://mathoverflow.net/questions/101463/properties-of-natural-numbers-such-that-there-is-a-very-large-largest-number-w
[6] Prime factors of 2025 - Math Tools
https://math.tools/numbers/prime-factors/2025
[7] Do you know this The number 2025 can be represented ... - Threads
https://www.threads.net/@data.science.beginners/post/DD7WsWTTuaP
[8] what is special about the number 2025? - hellosunday.ca
https://hellosunday.ca/Vierte4/what-is-special-about-the-number-2025
Tony
>
>
--
Mob:04 3365 2400 Email: [email protected], [email protected]
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Message: 3
Date: Tue, 24 Dec 2024 14:26:19 +0000
From: Stephen Loosley <[email protected]>
To: "[email protected]" <[email protected]>
Subject: [LINK] US launches probe into semiconductor industry
Message-ID:
<sy5p282mb44095d8ed162e15ad95a634cc2...@sy5p282mb4409.ausp282.prod.outlook.com>
Content-Type: text/plain; charset="Windows-1252"
Please Note: This email did not come from ANU, Be careful of any request to buy
gift cards or other items for senders outside of ANU. Learn why this is
important.
https://www.scamwatch.gov.au/types-of-scams/email-scams#toc-warning-signs-it-might-be-a-scam
US launches probe into Chinese semiconductor industry
Investigation comes just weeks before Biden administration hands over to
president-elect Donald Trump
By Tim Bradshaw and Jonathan Wheatley in London and Edward White in Shanghai
and Nian Liu in Beijing yesterday
https://www.ft.com/content/072d391c-93af-40c6-b020-a4a36d31d4c8
The US has launched a probe into alleged anti-competitive measures by China to
support its semiconductor industry, just weeks before the Biden administration
hands over to president-elect Donald Trump.
The US Trade Representative?s office said it was investigating ?China?s acts,
policies and practices related to targeting of the semiconductor industry for
dominance?.
The probe will be conducted under Section 301 of the US Trade Act and initially
target what the USTR called ?foundational? semiconductors, including those used
by the automotive, healthcare, infrastructure, aerospace and defence industries.
It marks the latest in a worsening tit-for-tat trade war over semiconductors,
sparking fears of serious disruptions to international supply chains.
Potential outcomes of a Section 301 investigation include import restrictions
or new tariffs on shipments from China of the kinds of chips used in cars,
household appliances and consumer devices ? a decision that would fall to the
Trump administration.
Washington on Monday accused China of using ?extensive anti-competitive and
non-market means, including setting and pursuing market share targets, to
achieve indigenisation and self-sufficiency?. China?s alleged tactics were
designed to achieve dominance of the semiconductor industry in China and on
global markets, the USTR said.
After several years of focusing its semiconductor policies on the most
cutting-edge processors necessary for creating advanced artificial
intelligence, Washington is turning its attention more to the mature end of the
market, with chips manufactured using what the industry calls ?legacy?
production systems.
Makers of advanced chip manufacturing equipment, such as ASML, are already
restricted from selling their most sophisticated tools to Chinese chipmakers,
holding back China?s advances in AI and curtailing its efforts to build a rival
to Silicon Valley-based Nvidia.
However, that has not prevented Chinese chipmakers from making huge investments
to scale up production of legacy semiconductors. Some analysts estimate that
China is on track to double its chip manufacturing capacity by the end of the
decade, boosted by subsidies from Beijing.
The commerce ministry in Beijing said it was ?firmly opposed? to the latest 301
investigation, and that action would disrupt global supply chains and hurt the
interest of US companies and global consumers.
It noted that US companies dominate the global chip market and the US
government has provided ?huge? subsidies to its domestic chip industry. Beijing
also issued a thinly veiled warning of retaliation, saying China would ?take
all necessary measures? to defend its rights.
US and European semiconductor executives have warned that local chipmakers
could suffer from the same kind of problems that the flood of low-cost Chinese
solar panel imports has caused western producers in recent years. Relying on
Chinese suppliers could also create national security issues for the US,
officials fear.
Recommended:
Chris Miller: Western nations need a plan for when China floods the chip market
Often overlooked amid the hype around AI, the significance of legacy
semiconductors became apparent during the Covid-19 pandemic, when factory
shutdowns triggered widespread shortages of everyday electronic goods.
A report by the US Department of Commerce earlier this month found that China?s
recent increase in production of mature-node semiconductors ?has already begun
to cause pricing pressure that may weaken US chip suppliers? competitive
positions?.
More than two-thirds of US companies? products use chips produced in Chinese
foundries, the report said.
China has for decades viewed its dependence on the US and other countries as a
fundamental national security vulnerability. But it has struggled to shake its
reliance on foreign companies for the key design and manufacturing technologies
needed to make increasingly sophisticated chips.
Earlier this month, Washington issued new export controls targeting China?s
ability to make the most advanced chips, including tougher restrictions on
shipping semiconductor manufacturing tools and a ban on exports of advanced
memory chips needed in AI hardware.
Beijing swiftly hit back, banning the shipment to the US of key minerals and
metals used in chip production. It also opened its own investigation into
Nvidia for suspected violations of the country?s anti-monopoly law.
--
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