[Merged by Bors] - feat(Geometry/Euclidean/Altitude): altitudeFoot, height

[jsm28]

As discussed in #23752, add definitions for the foot of an altitude of a simplex and the height of a vertex of a simplex. Provide a minimal linkage to the definition of altitude (for example, altitudeFoot lies in the altitude). No change is made to the definition or existing API for altitude. (In particular, that definition uses an older style of {n : ℕ} (s : Simplex ℝ P (n + 1)) where faceOpposite and altitudeFoot use the newer approach of {n : ℕ} [NeZero n] (s : Simplex ℝ P n).)

The existing lemmas ne_orthogonalProjection_faceOpposite and dist_orthogonalProjection_faceOpposite_pos are changed to be about altitudeFoot and height, renamed and moved. I think they are recent enough that no deprecations are needed.

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[github-actions]

PR summary baddfb7671

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Geometry.Euclidean.Altitude	1898	1901	+3 (+0.16%)

Import changes for all files

Files	Import difference
Mathlib.Geometry.Euclidean.Altitude	3

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Declarations diff

+ affineSpan_pair_altitudeFoot_eq_altitude
+ altitudeFoot
+ altitudeFoot_mem_affineSpan
+ altitudeFoot_mem_affineSpan_faceOpposite
+ altitudeFoot_mem_altitude
+ height
+ height_pos
+ ne_altitudeFoot
- dist_orthogonalProjection_faceOpposite_pos
- ne_orthogonalProjection_faceOpposite

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[eric-wieser]

No change is made to the definition or existing API for altitude. (In particular, that definition uses an older style of {n : ℕ} (s : Simplex ℝ P (n + 1)) where faceOpposite and altitudeFoot use the newer approach of {n : ℕ} [NeZero n] (s : Simplex ℝ P n).)

I think we should correct this, but no need to do so in this PR.

bors merge

Thanks!

[mathlib-bors]

Pull request successfully merged into master.

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