Using circles, discover pi for yourself.
Did you discover the math constant called "pi"?With a bit of close work, you can uncover the clever idea and source of the concept, as well as get its no-longer abstract meaning and find an approximate value.It is wrapped up in every sphere and circle, but where did you imagine it in the first place?There are detailed instructions for jumping into math discoveries.
Step 1: You should begin to understand the geometry of the circle in a plane.
The point, plane, and space are not defined in the study of geometry, but are described as they are used.What is a circle?One can learn a lot more as they go along with the following information.The points are equidistant from the center point.The point equidistant from any point of the circle is part of it, as is the segment between one endpoint at the center and the other end."The distance around circular-fence" is a long and odd word.
Step 2: You can discover your formula.
The diameter can be curved and placed end to end around the circle.Let's say that C is 3 X d.It was too easy to do, but now you will clean that idea up.Your "discovery" was a part of the expression of mathematical mysteries in ancient times.
Step 3: Take a rough idea of pi, about 3, and realize that it's not exactly three.
You will make it more accurate.
Step 4: There are different sizes of containers.
It's harder to measure than a globe or ball.
Step 5: You can get a non-kinky string and a meter-stick.
Step 6: You can make a chart or table.
quotient C / d is?.
Step 7: Measure around each item by wrapping a string around it.
The distance should be marked on the string.The distance around a circle is called the circumference, not the perimeter.
Step 8: Take the part of the string you marked as the distance around the circle and straighten it.
You can use decimals to write down your measurement.Since you would have needed to tighten the string around the object so that it was straight and extended to its full measure, you should pin or tape the ends.
Step 9: If you want to measure the diameter using decimals, you need to mark the center on the bottom and turn the container upside down.
Step 10: Measure across each circle exactly through the center of the four items with a straight edge measure.
The diameter is this.Multiplying by two times the radius.The 2 X radius is also written as 2r.
Step 11: Divide the circle's diameter by its circumference.
If your measurement is accurate, the four division problems of C / d are about 3 or 3.1.It's a ratio.It relates to the size.It is possible to use precise measurements using dividers, which are similar to a compass.
Step 12: If you average the four answers to the division problem by adding four quotients and dividing by four, you should get a more accurate result.
3.15 + 3.1 + 3.2 is equal to 4.That's 12.55 / 4 and can be rounded off to 3.14).That is the idea of "pi".The number of diameters is the constant.There is a number of diameters.The circle will fit a little more than 6 (2 times pi) times around it, as well as knowing that the diameter goes three times, so that's why the formula C is 2 X 3.14 X r."Yes!"If it's not crystal clear, read and think over it again.
Step 13: The diameter string can be used to cut the circumference string three times.
For each container, do this.The left-over piece of string will be the same length.The measurement length of this short piece of string should be.1415 which is just an example.
Step 14: Students should be helped to enjoy the exercise.
This could be a great turn-on moment, one of those moments where they feel like they understand.Wow!I like math more than I thought.This is a cross-curricular assignment and should be treated as a scientific experiment.
Step 15: If you are a teacher or tutor, you should make up an assignment sheet for your class.
Step 16: It's a hint a bit.
Do not let them show you, but tell them.Let them explore.The outcome is too easy for what it is showing.It should be made so that students can discover it as a mystery.Listen or read about an experiment.You wouldn't want to push straight through a reading or lecture presentation as here, but be subtle at first, facilitate, then clarify it after getting students to present their charts as posters of what they discovered.Students can post their presentations on a math wall, and be proud of their quick-wits, cleverness, working through it!
Step 17: For your students to take home as a project for extra credit outside math class, you can use this.
You might like to explore becoming a great teacher after you apply this one.
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