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No problem.
Regards,
Mark
How Many Right Angles Do Clock Hands Form in 12 Hours?
- Context: High School
- Thread starter joeyar
- Start date
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- Tags
- Theory
Click For Summary
Discussion Overview
The discussion revolves around the number of times the hands of a clock form right angles over a 12-hour period, focusing on the theoretical and mathematical aspects of the problem. Participants explore various methods of counting and reasoning about the angles formed by the hour and minute hands, while also considering the implications of starting points for the count.
Discussion Character
- Exploratory
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- Some participants suggest that the hands form right angles 23 times, depending on the starting point of the count.
- Others argue that if counting starts at specific times like 3:00 or 9:00, the number of right angles is 23, while starting at other times may yield only 22.
- A brute force method is mentioned, listing approximate times for right angles, with one participant claiming there are 22 occurrences.
- Mathematical approaches are presented, including the use of position vectors and angular velocities to derive the times at which right angles occur.
- Some participants express confusion about the inclusion of the second hand and its relevance to the problem.
- There is a discussion about the visibility of text used to hide solutions, indicating a meta-discussion about forum practices.
- One participant points out a potential oversight in counting, suggesting that a right angle occurs around 2:55, while another insists that the count remains at 22.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the exact number of right angles formed, with multiple competing views on the counting method and starting points. The discussion remains unresolved regarding the implications of different starting times on the total count.
Contextual Notes
Some participants note that the problem's complexity may depend on the definitions used and the specific starting times chosen for counting. The discussion includes various mathematical approaches, but there are unresolved steps and assumptions that affect the conclusions drawn.
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