#euclidea 搜索结果

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Happy Pi Day! 🥧🥧🥧 #euclidea #PiDay2025

#euclidea_puzzle_264 #euclidea 🎓 Given two circles A and B. The radius of circle A is twice the distance between the centers A and B. Construct two ⟂ diameters so that segments connecting their ends are parallel to AB. Try to complete in 12E. Task by Jane Summer🙏 #math

#euclidea_puzzle_263 #euclidea 🎓 Given 3 rays with a common vertex A and the point B. Construct a line through B so that the marked segments are equal. Try to complete the construction in 10 E-moves. Task by Jane Summer 🙏 #math #geometry

#euclidea_puzzle_262 #euclidea 🎓 3 circles are externally tangent to a common line and to each other. Construct a tangent to the smallest circle that cuts the other 2 so that the resulting chords are equal. Try to complete in 7 E-moves. Task by Jane Summer🙏 #math #geometry

#euclidea_puzzle_261 #euclidea 🎓 Two given circles have a common point of tangency. Construct a line through the end of their common diameter (point A) that cuts off equal chords on them. Try to do this in 6 moves. (this task was inspired by Jane Summer 🙏) #math #geometry

#euclidea_puzzle_260 #euclidea 🎓 On a diagonal of a regular octagon, a point is chosen such that an adjacent side is seen at angle of 75°. Find the angle x at which the opposite side is seen from this point. #math #geometry

#euclidea_puzzle_259 #euclidea 🎓 On two sides of a regular octagon, points are chosen such that each side is divided into two segments with lengths 1 and √√2, respectively. Find the angle x. #math #geometry

🎓 Proof: OE = OD = r√3, and AF is the perpendicular bisector of OE, so it lies at distance r√3/2 from O and cuts a chord of length r from the given circle. #xmath2024_01 #euclidea #maths #geometry

Xmath Contest 2024-01 Solution The cheapest $20 solution (by Anders Kaseorg) 🤓 🎓 Construct a line through the point A with a chord inside the circle equal to its radius. Find the cheapest possible solution if a line costs $5 and a circle costs $3. #euclidea #xmath2024_01

❄️ The square of the sum of consecutive numbers starting from 1 equals the sum of their cubes. Is this always true, or is it a magical coincidence for #2025? #maths #2025puzzle #euclidea

#euclidea_puzzle_258 #euclidea 🎓 Find the angle x in the given regular octagon if the green triangle is on the side of the blue square. #math #geometry

❄️ Find the integer radius of a circle that encloses exactly 2025 unit squares and has its center at the center of a square. #maths #2025puzzle #euclidea

❄️ Find a 4-digit square number that becomes another square number when each digit is increased by 1. #maths #2025puzzle #euclidea

#euclidea_puzzle_257 #euclidea 🎓 Find the angle x in the given regular octagon if the three red segments are equal. #math #geometry

❄️ In which numeral systems 2025 is a palindrome? #maths #puzzle #euclidea

#euclidea_puzzle_256 #euclidea 🎓 A point is chosen inside a regular octagon such that two of the angles shown in the picture are right angles. What can be the angle x? Find all possible values. New series of tasks "Regular octagons" 🤓 #math #geometry

❄️☃️❄️ Express 2025 using the same digit (5, 7 or 8) and arithmetic operations +, -, *, /, ^, factorial !, square root √, and brackets. The picture contains a hint about the minimum quantity of numbers. #maths #euclidea #puzzle #problem #solution

Happy Pi Day! 🥧🥧🥧 #euclidea #PiDay2025

❄️ Xmath Contest 2024 - 05 Construct the diameter of a circle that is parallel to a given line using only a straightedge. Details about the contest see in comments 👇#euclidea #xmath

#euclidea_puzzle_257 #euclidea 🎓 Find the angle x in the given regular octagon if the three red segments are equal. #math #geometry

#euclidea_puzzle_259 #euclidea 🎓 On two sides of a regular octagon, points are chosen such that each side is divided into two segments with lengths 1 and √√2, respectively. Find the angle x. #math #geometry

❄️☃️❄️ Express 2025 using the same digit (5, 7 or 8) and arithmetic operations +, -, *, /, ^, factorial !, square root √, and brackets. The picture contains a hint about the minimum quantity of numbers. #maths #euclidea #puzzle #problem #solution

❄️ In which numeral systems 2025 is a palindrome? #maths #puzzle #euclidea

#euclidea_puzzle_261 #euclidea 🎓 Two given circles have a common point of tangency. Construct a line through the end of their common diameter (point A) that cuts off equal chords on them. Try to do this in 6 moves. (this task was inspired by Jane Summer 🙏) #math #geometry

❄️ Xmath Contest 2024 - 04 🎓 Given a right angle and the point A inside it. Construct two equal circles tangent to the sides of the angle and to each other at A. Details about the contest see in comments 👇 #euclidea #xmath

#euclidea_puzzle_264 #euclidea 🎓 Given two circles A and B. The radius of circle A is twice the distance between the centers A and B. Construct two ⟂ diameters so that segments connecting their ends are parallel to AB. Try to complete in 12E. Task by Jane Summer🙏 #math

#euclidea_puzzle_260 #euclidea 🎓 On a diagonal of a regular octagon, a point is chosen such that an adjacent side is seen at angle of 75°. Find the angle x at which the opposite side is seen from this point. #math #geometry

#euclidea_puzzle_256 #euclidea 🎓 A point is chosen inside a regular octagon such that two of the angles shown in the picture are right angles. What can be the angle x? Find all possible values. New series of tasks "Regular octagons" 🤓 #math #geometry

#euclidea_puzzle_263 #euclidea 🎓 Given 3 rays with a common vertex A and the point B. Construct a line through B so that the marked segments are equal. Try to complete the construction in 10 E-moves. Task by Jane Summer 🙏 #math #geometry

#euclidea_puzzle_262 #euclidea 🎓 3 circles are externally tangent to a common line and to each other. Construct a tangent to the smallest circle that cuts the other 2 so that the resulting chords are equal. Try to complete in 7 E-moves. Task by Jane Summer🙏 #math #geometry

❄️ Find a 4-digit square number that becomes another square number when each digit is increased by 1. #maths #2025puzzle #euclidea

❄️ Find the integer radius of a circle that encloses exactly 2025 unit squares and has its center at the center of a square. #maths #2025puzzle #euclidea

#euclidea_puzzle_258 #euclidea 🎓 Find the angle x in the given regular octagon if the green triangle is on the side of the blue square. #math #geometry

❄️❄️❄️ Xmath 2024 is over. And we are ready to announce our winners! 1st place: Jane Summer 2nd place: Anders Kaseorg 3rd place: Diana Glazova 4th place: Alexey Vladimirovich Congratulations! 🎉 #xmath #winners #euclidea

❄️ The square of the sum of consecutive numbers starting from 1 equals the sum of their cubes. Is this always true, or is it a magical coincidence for #2025? #maths #2025puzzle #euclidea