Circumference and Pi
Read this topicExplanations 1
- Let's explore what the relation is between the circumference and diameter. You may already know the relation, Circumference=π⋅diameter\text{Circumference} = \pi \cdot \text{diam…
By Ray Li, Mihir Singhal, Tristan Pollner, Tom Shen, Avi Romanoff, Expii Team, Garrison Taylor, Alex Federspiel
Problems 21
- Now imagine that the rope is lifted at all points simultaneously, so that it floats above the Earth at the same height all along its length. What is the largest thing that could…
- You have traveled west on the Oregon Trail, survived dysentery, and have staked your claim on a new plot of land. You have 4 miles of fence which you can put in any shape you'd …
- Mathematical objects appear everywhere, from manmade architecture to nature. Spring is here, and plants are flowering again! Which mathematical object appears in ferns, sunflowe…
- On October 12, 1492, after departing from the Canary Islands, Christopher Columbus sighted land which he mistook for an island off the coast of China, but in reality was what we…
- Here is a slightly modified problem from the 2015 AMC: A clock with diameter 4x and a disk with diameter 2x are tangent at the 12 o' clock point on the clock face. An arrow on t…
- 227\frac{22}{7}722 is often used as an approximation for π\piπ. What is the percent error for this approximation?
- 3.14 is often used as an approximation for π\piπ. What is the percent error of this approximation?
- Which of the following are true?
- Which of the following is the best approximation for π\piπ?
- Another quantity commonly used in circle geometry is τ\tauτ, which is equal to 2π2\pi2π. Which of the following (if any) are also equal to τ\tauτ?
- A radian is an angle measure that corresponds with an arclength of r on a circle with radius r. How many radians are in a circle?
- There is a highway that wraps around a large lake, making a 90-degree turn through a gradual curve with follows the arc of a perfect circle. Each direction has 5 lanes for traff…
- What is the time delay between when she speaks and when she hears her echo?
- The radius of the Earth is 6371 km. The radius of an average blue marble is ½ cm. If the circumference of the Earth is actually 40075 km, how many digits of pi do you need to ca…
- Circle AAA has circumference CAC_ACA and radius RAR_ARA. Circle BBB has circumference CBC_BCB and radius RBR_BRB. Which (if any) of the following are true?
- A giant pie has a radius of 1 yard. Approximately how many regular pies (with diameter of 1 foot) would fit along the outer rim of a giant pie?
- Which of the following depend on pi?
- Which of the following expressions (if any) are equal to π\piπ?
- Which of the following are true about π\piπ?
- Radians are units to measure the sizes of angles. 1 radian is the central angle of an arc whose length is the same as the radius of the circle. How many radians are in a circle?
- Suppose you have a circle where the magnitude of the radius (i.e. the value without the units) is equal to the magnitude of the area. What is the radius?