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Eggs in a Basket
There is a basket with a certain number of eggs. If the eggs are taken from the basket two at a time, only one egg remains. 
Statistics Calculator with Python
By: Tao Steven Zheng (郑涛) 1 def statistics(samples): 2 3 N= len(samples) 4 mean= sum(samples)/ N 5 sum_squares= sum((meanx)**2 for x in samples) 6 stan_dev= (sum 
Zheng's Problem Solving Process
There are five steps to problem solving: 1) understanding 
Four Circle Theorem
Suppose there are four circles lying in a plane, such that each circle is mutually tangent to the other three circles. Let the radius of each circle be. Prove that Hint: Given three angles where 
Jiuzhang Suanshu (Gougu 6)
This classic problem from the Jiuzhang Suanshu (九章算术) is called Reed in a Pond (池中葭). 今有池方一丈，葭生其中央，出水一尺 
Hundred Fowls Problem with Python
By: Tao Steven Zheng (郑涛) Description Hundred Fowls Problem: An indeterminate system of linear equations in the form 
Quantum Measurements
Let there be two operators and that represent their respective observables and. has two eigenvalues and, each corresponding to respective normalized eigenstates: 
Emperor Kangxi on Mathematics and Astronomy
Emperor Kangxi (1654  1722, reigned 1661  1722) was an avid learner. He learned mathematics and astronomy from the Jesuit missionaries who visited Peking (Beijing). The following excerpt is from a diary of Emperor Kangxi called 
Sunzi Suanjing (Lower Scroll 26)
今有物，不知其數。三、三數之，賸二；五、五數之，賸三；七、七數之，賸二。問：物幾何？ Suppose we have an unknown number 
Magnetic Compass 指南针
【今译】 看风水的人用磁石去磨针尖，针尖就能指出南方，不过常常略为偏东，并不完全 
Annuities
An annuity is a series of regular payments that are put into an investment that grows with compounded interest (essentially the sum of compound interest over time). Most books state the annuity formula as Part 
Berlin Papyrus Problem 1
The Berlin Mathematical Papyrus, or Berlin Papyrus 6619, is an ancient Egyptian mathematics document dating to roughly 1800 BCE. The readable fragments were published by Hans SchackSchackenburg in 1900 and 1902. The surviving fragments 
Atomic Electrostatics
This problem is an investigation of Rutherford's model of the atom. Although this model is considered primitive to modern standards, it provides a fairly accurate approximation of the electrostatics of the atom. Consider an 
Zhang Qiujian Suanjing (Lower scroll 14)
今有甲、乙、丙三人持錢不知多少。甲言：“我得乙太半，得丙少半，可滿一百。”乙言：“我得 甲太半 
Balancing with Geometry
An isosceles triangle is to be cut from a square plate of uniform density, and width (as shown below). What is the height of the removed isosceles triangle such that the resulting shape balances at 
The Venturimeter
Consider an ideal fluid of density flowing through a horizontal pipe of variable crosssectional area. The fluid at the portion of the pipe with crosssectional area is moving at and has a measured 
Prismoidal Formula
A prismatoid is a polyhedron whose vertices all lie in one or the other of two parallel planes. The perpendicular distance between the two planes is called the height or altitude of the prismatoid. The 
Calendrics with Python
By: Tao Steven Zheng (郑涛) This program takes in three inputs (string, int, int) and outputs a string. The purpose is to input day1, day2, and the weekday of day1 in order to report 
Thales' Circle Theorem
Let there be a triangle inscribed in a circle such that the longest side of the triangle forms the diameter of the circle. Show that the triangle is a right triangle. Let be the diameter 
Current Carrying Wires
Consider two currentcarrying wires, one with current, and one with current. Using the righthand rule, one can determine the direction of the magnetic fields across each wire. The righthand rule is also 
Atmospheric Thermodynamics
Consider the following information. Solar constant: 
Empirical Formula
A blue powdered substance is found to be made of 25.3% copper, 12.9% sulfur, 25.7% oxygen, and 36.1% water. Determine the empirical formula of this substance. Consider only 100 grams of 
Forced Oscillations and Resonance
A 1 kg object is attached to spring that would stretch the spring 1 m by a force of 1 N. There is no damping in the system and a forcing function of the form 
Harmonic Series
The harmonic series is an infinite series given by the sum of reciprocals. Part 1: Use the comparison test to prove that the harmonic series is divergent. 
Hailstone Numbers with Python
By: Tao Steven Zheng (郑涛) The unproven Collatz conjecture states that the hailstone sequence for any starting positive integer always terminates (by reaching 1). This sequence was named by Lothar Collatz (1910  1990) in
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