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29/10/2026

𝗢𝗡𝗖𝗘 𝗨𝗣𝗢𝗡 𝗔 𝗠𝗔𝗧𝗛𝗘𝗠𝗔𝗧𝗜𝗖𝗜𝗔𝗡 #𝟴

𝓓𝓸 𝔂𝓸𝓾 𝓴𝓷𝓸𝔀 𝓽𝓱𝓮 𝓶𝓪𝓽𝓱𝓮𝓶𝓪𝓽𝓲𝓬𝓲𝓪𝓷 𝔀𝓱𝓸 𝓬𝓸𝓷𝓷𝓮𝓬𝓽𝓮𝓭 𝓪𝓵𝓰𝓮𝓫𝓻𝓪 𝓪𝓷𝓭 𝓰𝓮𝓸𝓶𝓮𝓽𝓻𝔂?🤔

Meet 𝗥𝗲𝗻é 𝗗𝗲𝘀𝗰𝗮𝗿𝘁𝗲𝘀, a French philosopher and mathematician who studied arithmetic, geometry, astronomy, and mechanics. His interest in mathematics became the foundation for much of his later work.

One of his most important mathematical works was 𝙇𝙖 𝙂é𝙤𝙢é𝙩𝙧𝙞𝙚. In this work, he applied algebra to geometry and developed ideas that became the foundation of Cartesian, or analytic, geometry.

Descartes demonstrated how algebra could be used to investigate geometric problems. This made it possible to represent geometric relationships using equations, establishing an important foundation for modern analytic geometry.

𝙏𝙝𝙚 𝙛𝙖𝙢𝙞𝙡𝙞𝙖𝙧 𝘾𝙖𝙧𝙩𝙚𝙨𝙞𝙖𝙣 𝙘𝙤𝙤𝙧𝙙𝙞𝙣𝙖𝙩𝙚 𝙨𝙮𝙨𝙩𝙚𝙢 𝙞𝙨 𝙖𝙨𝙨𝙤𝙘𝙞𝙖𝙩𝙚𝙙 𝙬𝙞𝙩𝙝 𝘿𝙚𝙨𝙘𝙖𝙧𝙩𝙚𝙨 𝙗𝙚𝙘𝙖𝙪𝙨𝙚 𝙤𝙛 𝙝𝙞𝙨 𝙬𝙤𝙧𝙠 𝙘𝙤𝙣𝙣𝙚𝙘𝙩𝙞𝙣𝙜 𝙖𝙡𝙜𝙚𝙗𝙧𝙖 𝙖𝙣𝙙 𝙜𝙚𝙤𝙢𝙚𝙩𝙧𝙮.📈

𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲𝘀:
O’Connor, J. J., & Robertson, E. F. (1996). René Descartes. MacTutor History of Mathematics Archive, University of St Andrews.
https://mathshistory.st-andrews.ac.uk/Biographies/Descartes/

Wild Maths. (n.d.). René Descartes and the fly on the ceiling. Wild Maths.
https://wild.maths.org/rené-descartes-and-fly-ceiling

27/10/2026

𝗠𝗔𝗧𝗛-𝗘𝗥 𝗢𝗙 𝗙𝗔𝗖𝗧 #𝟴
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‎𝓓𝓲𝓭 𝔂𝓸𝓾 𝓴𝓷𝓸𝔀? 🧐

‎Any two consecutive Fibonacci numbers have a greatest common divisor (GCD) of 1.

𝟮𝟭 𝗮𝗻𝗱 𝟯𝟰 → 𝗚𝗖𝗗 = 𝟭
𝟯𝟰 𝗮𝗻𝗱 𝟱𝟱 → 𝗚𝗖𝗗 = 𝟭

‎𝗖𝗼𝗻𝘀𝗲𝗰𝘂𝘁𝗶𝘃𝗲 𝗶𝗻 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲, 𝗿𝗲𝗹𝗮𝘁𝗶𝘃𝗲𝗹𝘆 𝗽𝗿𝗶𝗺𝗲 𝗯𝘆 𝗻𝗮𝘁𝘂𝗿𝗲! 🤯
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‎Did you know that 𝗮𝗻𝘆 𝘁𝘄𝗼 𝗰𝗼𝗻𝘀𝗲𝗰𝘂𝘁𝗶𝘃𝗲 𝗙𝗶𝗯𝗼𝗻𝗮𝗰𝗰𝗶 𝗻𝘂𝗺𝗯𝗲𝗿𝘀 𝗮𝗿𝗲 𝗿𝗲𝗹𝗮𝘁𝗶𝘃𝗲𝗹𝘆 𝗽𝗿𝗶𝗺𝗲? This means that their 𝗴𝗿𝗲𝗮𝘁𝗲𝘀𝘁 𝗰𝗼𝗺𝗺𝗼𝗻 𝗱𝗶𝘃𝗶𝘀𝗼𝗿 (𝗚𝗖𝗗)—the largest positive integer that divides both numbers exactly—is always 𝟭!
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‎For example, 𝟮𝟭 𝗮𝗻𝗱 𝟯𝟰 have no common factor other than 1. The same is true for
‎𝟯𝟰 𝗮𝗻𝗱 𝟱𝟱, as well as every other pair of consecutive Fibonacci numbers. No matter how far you go in the sequence, this fascinating mathematical property remains true!
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‎Isn't it amazing how a simple number pattern can reveal such an interesting relationship? The 𝗙𝗶𝗯𝗼𝗻𝗮𝗰𝗰𝗶 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 is more than just a series of numbers; it also shows how 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗽𝗮𝘁𝘁𝗲𝗿𝗻𝘀 𝗳𝗼𝗹𝗹𝗼𝘄 𝗿𝗲𝗺𝗮𝗿𝗸𝗮𝗯𝗹𝗲 𝗿𝘂𝗹𝗲𝘀 𝗮𝗻𝗱 𝗰𝗼𝗻𝗻𝗲𝗰𝘁𝗶𝗼𝗻𝘀. It reminds us that even ordinary-looking numbers can hold extraordinary mathematical facts! 💡📚
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‎So, the next time you encounter two consecutive Fibonacci numbers, remember—they may be different in value,
‎𝗯𝘂𝘁 𝘁𝗵𝗲𝗶𝗿 𝗼𝗻𝗹𝘆 𝗰𝗼𝗺𝗺𝗼𝗻 𝗳𝗮𝗰𝘁𝗼𝗿 𝗶𝘀 𝟭! 🔢✨📚
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‎𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲:
‎Weisstein, E. W. (n.d.). Fibonacci number. Wolfram MathWorld. https://mathworld.wolfram.com/FibonacciNumber.html
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26/10/2026

𝗕𝗘𝗖𝗔𝗨𝗦𝗘 𝗪𝗘 𝗡𝗘𝗘𝗗 𝗠𝗢𝗥𝗘 𝗧𝗛𝗔𝗡 𝗝𝗨𝗦𝗧 𝗚𝗢𝗢𝗗 𝗚𝗥𝗔𝗗𝗘𝗦. 📚

Amid the demands of academics, deadlines, and our everyday responsibilities, we all need a moment to pause and reconnect with what truly matters. Sometimes, all we need is a little time to worship, share our faith, and be reminded that we do not have to go through every season alone.

With this, the 𝗦𝗼𝗰𝗶𝗲𝘁𝘆 𝗼𝗳 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀 𝗘𝗻𝘁𝗵𝘂𝘀𝗶𝗮𝘀𝘁𝘀 (𝗦𝗠𝗘), together with 𝗦𝗘𝗔𝗟, 𝗟𝗜𝗞𝗔𝗦, 𝗮𝗻𝗱 𝗖𝗵𝗶 𝗔𝗹𝗽𝗵𝗮 𝗦𝘁𝘂𝗱𝗲𝗻𝘁 𝗠𝗶𝗻𝗶𝘀𝘁𝗿𝘆, invites you to 𝗔𝗰𝗮𝗱𝗲𝗺𝗶𝗰 𝗪𝗼𝗿𝘀𝗵𝗶𝗽 & 𝗙𝗲𝗹𝗹𝗼𝘄𝘀𝗵𝗶𝗽 2026, carrying the theme “𝙍𝙤𝙤𝙩𝙚𝙙 𝙞𝙣 𝙁𝙖𝙞𝙩𝙝, 𝙍𝙞𝙨𝙞𝙣𝙜 𝙞𝙣 𝙀𝙭𝙘𝙚𝙡𝙡𝙚𝙣𝙘𝙚” based on 𝑪𝒐𝒍𝒐𝒔𝒔𝒊𝒂𝒏𝒔 2:7.

📅 𝗢𝗰𝘁𝗼𝗯𝗲𝗿 29, 2026 (𝗧𝗵𝘂𝗿𝘀𝗱𝗮𝘆)
⏰ 4:00 𝗣𝗠 – 7:00 𝗣𝗠
📍 4𝘁𝗵 𝗙𝗹𝗼𝗼𝗿, 𝗗𝗘𝗩𝗖𝗢𝗠 𝗕𝘂𝗶𝗹𝗱𝗶𝗻𝗴

Let’s take this time to step away from our busy schedules, gather in His presence, and enjoy a meaningful time of worship and fellowship with one another. We hope to see you there!

22/10/2026

𝗥𝗜𝗖𝗔 𝗝𝗢𝗬 𝗧𝗢 𝗧𝗛𝗘 𝗪𝗢𝗥𝗟𝗗! 🌎🎶

Today, we’re celebrating our 𝐒𝐌𝐄 𝐕𝐢𝐜𝐞 𝐏𝐫𝐞𝐬𝐢𝐝𝐞𝐧𝐭, 𝐑𝐈𝐂𝐀 𝐉𝐎𝐘 𝐓𝐀𝐘𝐏𝐈𝐍!🥳

Thank you for being part of the team and for sharing your time, effort, and ideas with the 𝗦𝗼𝗰𝗶𝗲𝘁𝘆 𝗼𝗳 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀 𝗘𝗻𝘁𝗵𝘂𝘀𝗶𝗮𝘀𝘁𝘀. We appreciate the work you do and the role you play in making our organization better.

We hope you get to 𝒆𝒏𝒋𝒐𝒚 your day, 𝒔𝒑𝒆𝒏𝒅 𝒕𝒊𝒎𝒆 with your favorite people, and 𝒕𝒂𝒌𝒆 a well-deserved break from all the school and org responsibilities.

𝑾𝒊𝒔𝒉𝒊𝒏𝒈 𝒚𝒐𝒖 𝒂 𝒚𝒆𝒂𝒓 𝒇𝒊𝒍𝒍𝒆𝒅 𝒘𝒊𝒕𝒉 𝒎𝒐𝒓𝒆 𝒈𝒐𝒐𝒅 𝒕𝒉𝒊𝒏𝒈𝒔, 𝒏𝒆𝒘 𝒐𝒑𝒑𝒐𝒓𝒕𝒖𝒏𝒊𝒕𝒊𝒆𝒔, 𝒂𝒏𝒅 𝒎𝒆𝒎𝒐𝒓𝒊𝒆𝒔 𝒘𝒐𝒓𝒕𝒉 𝒌𝒆𝒆𝒑𝒊𝒏𝒈.

𝙔𝙤𝙪𝙧 𝙎𝙈𝙀 𝙁𝙖𝙢𝙞𝙡𝙮 𝙘𝙚𝙡𝙚𝙗𝙧𝙖𝙩𝙚𝙨 𝙬𝙞𝙩𝙝 𝙮𝙤𝙪!❤

22/10/2026

𝗢𝗡𝗖𝗘 𝗨𝗣𝗢𝗡 𝗔 𝗠𝗔𝗧𝗛𝗘𝗠𝗔𝗧𝗜𝗖𝗜𝗔𝗡 #𝟴 🌟

𝓓𝓸 𝔂𝓸𝓾 𝓴𝓷𝓸𝔀 𝓽𝓱𝓮 𝓶𝓪𝓽𝓱𝓮𝓶𝓪𝓽𝓲𝓬𝓲𝓪𝓷 𝔀𝓱𝓸 𝓭𝓲𝓼𝓬𝓸𝓿𝓮𝓻𝓮𝓭 𝓽𝓱𝓪𝓽 𝓪𝓷 𝓪𝓷𝓰𝓵𝓮 𝓯𝓸𝓻𝓶𝓮𝓭 𝓫𝔂 𝓪 𝓭𝓲𝓪𝓶𝓮𝓽𝓮𝓻 𝓸𝓯 𝓪 𝓬𝓲𝓻𝓬𝓵𝓮 𝓲𝓼 𝓪𝓵𝔀𝓪𝔂𝓼 𝓪 𝓻𝓲𝓰𝓱𝓽 𝓪𝓷𝓰𝓵𝓮?

Meet 𝗧𝗵𝗮𝗹𝗲𝘀 𝗼𝗳 𝗠𝗶𝗹𝗲𝘁𝘂𝘀, one of the earliest Greek mathematicians known for using logical reasoning to study geometry. Thales of Miletus lived around 620–546 BCE in Miletus, an ancient Greek city in Ionia. He was a mathematician, philosopher, astronomer, and engineer who explored different areas of knowledge.

Thales’s theorem states that when a triangle is inscribed in a circle and one side is the diameter, the angle opposite that diameter is a 90° angle. The theorem was later included and proved in Euclid’s Elements as Proposition 31 of Book III.

Thales’s theorem became an important result in Euclidean geometry, connecting circles, diameters, and right triangles. It can also be used in practical geometric constructions, such as finding the center of a circle and constructing a tangent to a circle.

Interesting fact about him, Thales was traditionally credited with predicting a solar eclipse in 585 BCE, although historians still debate exactly how he could have made the prediction. Another famous story says that he fell into a well while observing the stars, showing how deeply interested he was in astronomy.

𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲𝘀:
O’Grady, P. (n.d.). Thales of Miletus. Internet Encyclopedia of Philosophy. https://iep.utm.edu/thales/

Wikipedia contributors. (2026, September 14). Thales's theorem. Wikipedia. https://en.wikipedia.org/wiki/Thales%27s_theorem

21/10/2026

𝗢𝗥𝗗𝗘𝗥 𝗜𝗡 𝗧𝗛𝗘 𝗢𝗥𝗚, 𝗜𝗧'𝗦 𝗥𝗢𝗪𝗘𝗟𝗟𝗔'𝗦 𝗕𝗜𝗥𝗧𝗛𝗗𝗔𝗬! ⚖️

Today, we’re celebrating our 𝐒𝐌𝐄 𝐏𝐞𝐚𝐜𝐞 𝐎𝐟𝐟𝐢𝐜𝐞𝐫, 𝗥𝗢𝗪𝗘𝗟𝗟𝗔 𝗝𝗔𝗡𝗘 𝗙𝗘𝗥𝗡𝗔𝗡𝗗𝗢!🥳

Thank you for being part of the team and for sharing your time, effort, and ideas with the 𝗦𝗼𝗰𝗶𝗲𝘁𝘆 𝗼𝗳 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀 𝗘𝗻𝘁𝗵𝘂𝘀𝗶𝗮𝘀𝘁𝘀. We appreciate the work you do and the role you play in making our organization better.

We hope you get to 𝒆𝒏𝒋𝒐𝒚 your day, 𝒔𝒑𝒆𝒏𝒅 𝒕𝒊𝒎𝒆 with your favorite people, and 𝒕𝒂𝒌𝒆 a well-deserved break from all the school and org responsibilities.

𝑾𝒊𝒔𝒉𝒊𝒏𝒈 𝒚𝒐𝒖 𝒂 𝒚𝒆𝒂𝒓 𝒇𝒊𝒍𝒍𝒆𝒅 𝒘𝒊𝒕𝒉 𝒎𝒐𝒓𝒆 𝒈𝒐𝒐𝒅 𝒕𝒉𝒊𝒏𝒈𝒔, 𝒏𝒆𝒘 𝒐𝒑𝒑𝒐𝒓𝒕𝒖𝒏𝒊𝒕𝒊𝒆𝒔, 𝒂𝒏𝒅 𝒎𝒆𝒎𝒐𝒓𝒊𝒆𝒔 𝒘𝒐𝒓𝒕𝒉 𝒌𝒆𝒆𝒑𝒊𝒏𝒈.

𝙔𝙤𝙪𝙧 𝙎𝙈𝙀 𝙁𝙖𝙢𝙞𝙡𝙮 𝙘𝙚𝙡𝙚𝙗𝙧𝙖𝙩𝙚𝙨 𝙬𝙞𝙩𝙝 𝙮𝙤𝙪!❤

20/10/2026

𝗠𝗔𝗧𝗛-𝗘𝗥 𝗢𝗙 𝗙𝗔𝗖𝗧 #𝟳
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‎𝓓𝓲𝓭 𝔂𝓸𝓾 𝓴𝓷𝓸𝔀? 🧐
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‎𝗧𝗵𝗲 𝗻𝘂𝗺𝗯𝗲𝗿 𝟭 𝗮𝗽𝗽𝗲𝗮𝗿𝘀 𝗮𝘀 𝘁𝗵𝗲 𝗳𝗶𝗿𝘀𝘁 𝗱𝗶𝗴𝗶𝘁 𝗼𝗳 𝗻𝘂𝗺𝗯𝗲𝗿𝘀 𝗺𝘂𝗰𝗵 𝗺𝗼𝗿𝗲 𝗼𝗳𝘁𝗲𝗻 𝘁𝗵𝗮𝗻 𝘆𝗼𝘂 𝗺𝗶𝗴𝗵𝘁 𝗲𝘅𝗽𝗲𝗰𝘁! 👀🔢
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‎Imagine looking at a large collection of real-world numbers—such as populations, measurements, financial figures, or other data.
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‎You might expect the digits 𝟭 𝘁𝗵𝗿𝗼𝘂𝗴𝗵 𝟵 to appear as the first digit roughly equally often.
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‎But in many naturally occurring datasets, that isn't what happens.
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‎According to 𝗕𝗲𝗻𝗳𝗼𝗿𝗱’𝘀 𝗟𝗮𝘄, the digit 𝟭 appears as the leading digit about 𝟯𝟬.𝟭% 𝗼𝗳 𝘁𝗵𝗲 𝘁𝗶𝗺𝗲. The digit 𝟮 appears about 𝟭𝟳.𝟲%, while the digit 𝟵 appears only about 𝟰.𝟲%.
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‎The probabilities are given by the formula:
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‎𝙋(𝙙) = 𝙡𝙤𝙜₁₀(1 + 1/𝙙)
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‎where 𝗱 is the first digit from 1 to 9.
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‎For example:
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‎𝐏(𝟏) = 𝐥𝐨𝐠₁₀(𝟐) ≈ 𝟎.𝟑𝟎𝟏
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‎or about:
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‎𝟯𝟬.𝟭%🔢
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‎𝙎𝙤 𝙬𝙝𝙮 𝙙𝙤𝙚𝙨 𝙩𝙝𝙞𝙨 𝙝𝙖𝙥𝙥𝙚𝙣?
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‎Benford's Law is associated with datasets whose values span multiple orders of magnitude and have particular statistical properties.
‎𝗜𝘁 𝗱𝗼𝗲𝘀 𝗻𝗼𝘁 𝗮𝗽𝗽𝗹𝘆 𝘁𝗼 𝗲𝘃𝗲𝗿𝘆 𝗰𝗼𝗹𝗹𝗲𝗰𝘁𝗶𝗼𝗻 𝗼𝗳 𝗻𝘂𝗺𝗯𝗲𝗿𝘀, so it should not be treated as a universal rule for all data.
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‎The phenomenon was described by 𝗦𝗶𝗺𝗼𝗻 𝗡𝗲𝘄𝗰𝗼𝗺𝗯 𝗶𝗻 𝟭𝟴𝟴𝟭 and later investigated extensively by 𝗙𝗿𝗮𝗻𝗸 𝗕𝗲𝗻𝗳𝗼𝗿𝗱, whose 1938 paper helped establish it as the “law of anomalous numbers.”
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‎So, the next time you see a huge list of numbers, don't assume every digit has an equal chance of appearing first!
‎
‎𝗦𝗼𝗺𝗲𝘁𝗶𝗺𝗲𝘀, 𝟭 𝗿𝗲𝗮𝗹𝗹𝘆 𝗱𝗼𝗲𝘀 𝗰𝗼𝗺𝗲 𝗳𝗶𝗿𝘀𝘁. 👀
‎
‎𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲:
‎Weisstein, E. W. (n.d.). Benford's law. MathWorld—A Wolfram Resource.
‎https://mathworld.wolfram.com/BenfordsLaw.html
‎

15/10/2026

𝗢𝗡𝗖𝗘 𝗨𝗣𝗢𝗡 𝗔 𝗠𝗔𝗧𝗛𝗘𝗠𝗔𝗧𝗜𝗖𝗜𝗔𝗡 #𝟲 ⚫

𝓓𝓸 𝔂𝓸𝓾 𝓴𝓷𝓸𝔀 𝓽𝓱𝓮 𝓶𝓪𝓽𝓱𝓮𝓶𝓪𝓽𝓲𝓬𝓲𝓪𝓷 𝓫𝓮𝓱𝓲𝓷𝓭 𝓽𝓱𝓮 𝓼𝓽𝓾𝓭𝔂 𝓸𝓯 𝓹𝓪𝓻𝓪𝓫𝓸𝓵𝓪𝓼, 𝓮𝓵𝓵𝓲𝓹𝓼𝓮𝓼, 𝓪𝓷𝓭 𝓱𝔂𝓹𝓮𝓻𝓫𝓸𝓵𝓪? 🤔

Meet 𝗔𝗽𝗼𝗹𝗹𝗼𝗻𝗶𝘂𝘀 𝗼𝗳 𝗣𝗲𝗿𝗴𝗮, a Greek mathematician and astronomer who lived around the middle of the 3rd Century BCE. He became one of the most important geometers of ancient Greece through his systematic study of conic sections.

Apollonius studied mathematics in Alexandria and built upon the work of earlier mathematicians. His greatest work was Conics, an eight-book treatise that explored the properties of Parabolas, Ellipses, and Hyperbolas along with their tangents, diameters, and other geometric properties.

Apollonius made a major contribution to geometry by developing a systematic study of conic sections—the 𝒑𝒂𝒓𝒂𝒃𝒐𝒍𝒂, 𝒆𝒍𝒍𝒊𝒑𝒔𝒆, 𝒂𝒏𝒅 𝒉𝒚𝒑𝒆𝒓𝒃𝒐𝒍𝒂. His work in 𝘾𝙤𝙣𝙞𝙘𝙨 established many important properties of these curves and influenced later developments in geometry, astronomy, and mathematics. His study of conic sections also became an important foundation for later mathematicians studying curves and planetary motion.

One interesting fact is that these curves were already known before Apollonius. What made his work special was that he systematized and expanded the existing knowledge of conic sections. His work later influenced the development of advanced geometry and even mathematical astronomy.

𝙁𝙧𝙤𝙢 𝙘𝙪𝙧𝙫𝙚𝙨 𝙘𝙧𝙚𝙖𝙩𝙚𝙙 𝙗𝙮 𝙘𝙤𝙣𝙚𝙨 𝙩𝙤 𝙨𝙝𝙖𝙥𝙞𝙣𝙜 𝙩𝙝𝙚 𝙨𝙩𝙪𝙙𝙮 𝙤𝙛 𝙜𝙚𝙤𝙢𝙚𝙩𝙧𝙮, 𝘼𝙥𝙤𝙡𝙡𝙤𝙣𝙞𝙪𝙨 𝙡𝙚𝙛𝙩 𝙖 𝙡𝙖𝙨𝙩𝙞𝙣𝙜 𝙡𝙚𝙜𝙖𝙘𝙮 𝙞𝙣 𝙢𝙖𝙩𝙝𝙚𝙢𝙖𝙩𝙞𝙘𝙨, 𝙤𝙣𝙚 𝙘𝙪𝙧𝙫𝙚 𝙖𝙩 𝙖 𝙩𝙞𝙢𝙚. 🌟

𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲𝘀:

O’Connor, J. J., & Robertson, E. F. (1999). Apollonius. MacTutor History of Mathematics Archive, University of St. Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Apollonius/

Britannica Editors (2025, February 9). Apollonius of Perga. Encyclopedia Britannica. https://www.britannica.com/biography/Apollonius-of-Perga

13/10/2026

𝗠𝗔𝗧𝗛-𝗘𝗥 𝗢𝗙 𝗙𝗔𝗖𝗧 #𝟲
‎
‎𝓓𝓲𝓭 𝔂𝓸𝓾 𝓴𝓷𝓸𝔀? 🧐
‎
‎𝟬.𝟵𝟵𝟵… = 𝟭
‎
‎Yes, you read that correctly.
‎
‎𝟬.𝟵𝟵𝟵… 𝗶𝘀 𝗲𝘅𝗮𝗰𝘁𝗹𝘆 𝗲𝗾𝘂𝗮𝗹 𝘁𝗼 𝟭—𝗻𝗼𝘁 𝗮𝗽𝗽𝗿𝗼𝘅𝗶𝗺𝗮𝘁𝗲𝗹𝘆, 𝗯𝘂𝘁 𝗲𝘅𝗮𝗰𝘁𝗹𝘆! 🤯
‎
‎But there is an important detail: the dots (…) mean that the 9s continue 𝗳𝗼𝗿𝗲𝘃𝗲𝗿.
‎
‎For example:
‎
‎𝟬.𝟵 < 𝟭
‎𝟬.𝟵𝟵 < 𝟭
‎𝟬.𝟵𝟵𝟵 < 𝟭
‎
‎Every finite decimal with a limited number of 9s is less than 1.
‎
‎But when the 9s continue indefinitely:
‎
‎𝟬.𝟵𝟵𝟵… = 𝟭
‎
‎Here’s a simple algebraic proof:
‎
‎Let
‎
‎𝘅 = 𝟬.𝟵𝟵𝟵…
‎
‎Multiply both sides by 10:
‎
‎𝟭𝟬𝘅 = 𝟵.𝟵𝟵𝟵…
‎
‎Now subtract the first equation:
‎
‎𝟭𝟬𝘅 − 𝘅 = 𝟵.𝟵𝟵𝟵… − 𝟬.𝟵𝟵𝟵…
‎
‎So:
‎
‎𝟵𝘅 = 𝟵
‎
‎Divide by 9:
‎
‎𝘅 = 𝟭
‎
‎Since 𝘅 = 𝟬.𝟵𝟵𝟵…, we get:
‎
‎𝟬.𝟵𝟵𝟵… = 𝟭🎯
‎
‎Another way to understand it is through fractions. Since:
‎
‎‎𝟭/𝟯 = 𝟬.𝟯𝟯𝟯…
‎
‎multiplying both sides by 3 gives:
‎
‎𝟭 = 𝟬.𝟵𝟵𝟵…
‎
‎So 𝟬.𝟵𝟵𝟵… 𝗮𝗻𝗱 𝟭 𝗮𝗿𝗲 𝘀𝗶𝗺𝗽𝗹𝘆 𝘁𝘄𝗼 𝗱𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁 𝗱𝗲𝗰𝗶𝗺𝗮𝗹 𝗿𝗲𝗽𝗿𝗲𝘀𝗲𝗻𝘁𝗮𝘁𝗶𝗼𝗻𝘀 𝗼𝗳 𝘁𝗵𝗲 𝘀𝗮𝗺𝗲 𝗿𝗲𝗮𝗹 𝗻𝘂𝗺𝗯𝗲𝗿.
‎
‎The interesting part?
‎
‎𝟬.𝟵𝟵𝟵𝟵 with only four 9s is NOT equal to 1.
‎
‎But 𝟬.𝟵𝟵𝟵𝟵…, with infinitely many 9s, 𝗜𝗦 𝗲𝘅𝗮𝗰𝘁𝗹𝘆 𝟭! ♾️
‎
‎𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲:
‎Math Is Fun. (n.d.). Does 0.999... = 1? https://www.mathsisfun.com/9recurring.html

11/10/2026

𝗣𝗢𝗩: 𝙉𝙖𝙜𝙝𝙪𝙣𝙖-𝙝𝙪𝙣𝙖 𝙣𝙖 𝙠𝙖 𝙠𝙪𝙣𝙜 𝙪𝙣𝙨𝙖𝙤𝙣 𝙥𝙖𝙜𝙥𝙖𝙨𝙖𝙧 𝙨𝙖 𝙢𝙞𝙙𝙩𝙚𝙧𝙢 𝙚𝙭𝙖𝙢𝙨 𝙣𝙜𝙖 𝙙𝙞𝙡𝙞 𝙢𝙖𝙜-𝙨𝙩𝙪𝙙𝙮. 😭

𝐌𝐢𝐝𝐭𝐞𝐫𝐦𝐬 𝐧𝐚, 𝐦𝐠𝐚 𝐌𝐚𝐭𝐡𝐢𝐧𝐢𝐤𝐬!

Ayaw kalimot sa 𝙥𝙖𝙜-𝙧𝙚𝙫𝙞𝙚𝙬, 𝙥𝙖𝙜-𝙖𝙢𝙥𝙤, ug syempre, sa atong 𝙂𝙊𝙊𝘿 𝙇𝙐𝘾𝙆, 𝘽𝘼𝘽𝙔! 💋🍀

May the odds be ever in your favor, Mathiniks! Amping mo, trust your preparation, and manifesting taas nga scores for everyone. 𝗞𝗮𝘆𝗮 𝗿𝗮 𝗻𝗮 𝗻𝗶𝗻𝘆𝗼! ❤

𝗧𝗵𝗶𝗻𝗸. 𝗖𝗮𝗹𝗰𝘂𝗹𝗮𝘁𝗲. 𝗘𝗹𝗲𝘃𝗮𝘁𝗲.

🎥 𝗩𝗶𝗱𝗲𝗼 𝗖𝗿𝗲𝗱𝗶𝘁𝘀: 𝘋𝘳. 𝘈𝘯𝘵𝘩𝘰𝘯𝘺 𝘠𝘰𝘶𝘯 𝘷𝘪𝘢 𝘍𝘢𝘤𝘦𝘣𝘰𝘰𝘬

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