My lecturer says that a translation of the unit circle is not an isometry because then it’s no longer a bijection to itself (smth like that).

But if that’s true then how can a translation be an isometry? I’ve attached the example because I can’t understand when a translation is an isometry and when it isn’t.

But if that’s true then how can a translation be an isometry? I’ve attached the example because I can’t understand when a translation is an isometry and when it isn’t.

Original post by Y2_UniMaths

My lecturer says that a translation of the unit circle is not an isometry because then it’s no longer a bijection to itself (smth like that).

But if that’s true then how can a translation be an isometry? I’ve attached the example because I can’t understand when a translation is an isometry and when it isn’t.

But if that’s true then how can a translation be an isometry? I’ve attached the example because I can’t understand when a translation is an isometry and when it isn’t.

An isometry of a set is a distance-preserving map of the set to itself - it's commonly also required to be a bijection.

A translation is an isometry of the plane, but a translation would move the circle to a different circle. You could call that an isometry between the two different circles.

But any isometry of a single circle has to map the circle to the circle, not somewhere else.

(edited 7 months ago)

- Maths a level- can anyone help
- GCSE Edexcel Maths - trigonometric ratios of angles between 0 and 360
- Struggling with Year 2 pure maths
- Circular motion question help
- Wjec AS MATHS unit 1
- Mathematics for PAT Question Help
- Unit 3 applied science May 2024
- Maths A Level Coordinate Geometry Question
- Need help with this A Level Maths C6 Question
- biology question
- CAST diagram help
- WJEC Unit 1 Maths As Level Discussion 15 May 2024
- WJEC GCSE Mathematics Unit 1 Higher (3300U50-1) - 16th May 2024 [Exam Chat]
- Using complex numbers to plot coordinates
- CIE AS Level MCQ
- A Level Maths Trig Question
- London Accomodation
- Getting from a 5 -> 6 in maths within a week
- Can someone give me some advice please??
- Applying for Glasgow University's English Literature MA

Last reply 2 days ago

Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths

72

Last reply 2 days ago

Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths

72